{"id":178162,"date":"2024-02-28T14:58:08","date_gmt":"2024-02-28T13:58:08","guid":{"rendered":"https:\/\/datascientest.com\/en\/?p=178162"},"modified":"2024-02-11T18:30:54","modified_gmt":"2024-02-11T17:30:54","slug":"how-do-you-determine-the-primitive-of-a-function","status":"publish","type":"post","link":"https:\/\/datascientest.com\/en\/how-do-you-determine-the-primitive-of-a-function","title":{"rendered":"How do you determine the primitive of a function?"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"178162\" class=\"elementor elementor-178162\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ac41f06 e-flex e-con-boxed e-con\" data-id=\"ac41f06\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-09873bc elementor-widget elementor-widget-heading\" data-id=\"09873bc\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Calculating integrals is a regular part of mathematics, particularly for calculating probabilities, which is fundamental to data science. Generally, it is necessary to know a primitive of a function in order to calculate its integral. In this article, you will discover the definition of primitives and how do you determine the primitive of a function.\n<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2f89063 e-flex e-con-boxed e-con\" data-id=\"2f89063\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2cf7ff0 elementor-widget elementor-widget-heading\" data-id=\"2cf7ff0\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">What is the primitive of a function and how do you determine the primitive of a function?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-424dde6 elementor-widget elementor-widget-shortcode\" data-id=\"424dde6\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Let <span class=\"katex-eq\" data-katex-display=\"false\">\\left[a,b\\right]<\/span> be an interval, and <span class=\"katex-eq\" data-katex-display=\"false\">f : \\left[a,b\\right] \\to \\mathbb{R}<\/span> a function defined on the interval <span class=\"katex-eq\" data-katex-display=\"false\">\\left[a,b\\right]<\/span>. We say that <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> admits a primitive on <span class=\"katex-eq\" data-katex-display=\"false\">\\left[a,b\\right]<\/span> if there exists a differentiable function <span class=\"katex-eq\" data-katex-display=\"false\">F : \\left[a,b\\right]\\to \\mathbb{R}<\/span> such that for any <span class=\"katex-eq\" data-katex-display=\"false\">x \\in \\left]a,b\\right[<\/span>, <span class=\"katex-eq\" data-katex-display=\"false\">F^{\\prime}(x) = f(x)<\/span>. \nWe then say that <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> is a primitive of <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2dd8428 elementor-widget elementor-widget-shortcode\" data-id=\"2dd8428\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">For example, for <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = 3 x^2 + 5<\/span>, a primitive of <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> on <span class=\"katex-eq\" data-katex-display=\"false\">\\mathbb{R}<\/span> is <span class=\"katex-eq\" data-katex-display=\"false\">F(x) = x^3 + 5 x<\/span>. This can be verified by deriving <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span>.\nWe then say that <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> is a primitive of <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a93f7b8 elementor-widget elementor-widget-shortcode\" data-id=\"a93f7b8\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">The following table shows the primitives of some common functions.\nWe then say that <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> is a primitive of <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-da80c4b elementor-widget elementor-widget-image\" data-id=\"da80c4b\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/08\/primitive.png\" data-elementor-open-lightbox=\"yes\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MTcwNjI3LCJ1cmwiOmZhbHNlfQ%3D%3D\">\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/08\/primitive.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e832c73 elementor-hidden-desktop elementor-hidden-tablet elementor-widget elementor-widget-heading\" data-id=\"e832c73\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<span class=\"elementor-heading-title elementor-size-default\">Cliquez sur le tableau pour l'afficher en plein \u00e9cran.<\/span>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-5071a03 e-flex e-con-boxed e-con\" data-id=\"5071a03\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-57a4548 elementor-widget elementor-widget-heading\" data-id=\"57a4548\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Sufficient condition for the existence of a primitive\n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9dd762d elementor-widget elementor-widget-shortcode\" data-id=\"9dd762d\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Let <span class=\"katex-eq\" data-katex-display=\"false\">\\left[a,b\\right]<\/span> be an interval, and <span class=\"katex-eq\" data-katex-display=\"false\">f : \\left[a,b\\right] \\to \\mathbb{R}<\/span> a function defined on the interval <span class=\"katex-eq\" data-katex-display=\"false\">\\left[a,b\\right]<\/span>.\nWe then say that <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> is a primitive of <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-090e298 elementor-widget elementor-widget-shortcode\" data-id=\"090e298\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Let <span class=\"katex-eq\" data-katex-display=\"false\">\\left[a,b\\right]<\/span> be an interval, and <span class=\"katex-eq\" data-katex-display=\"false\">f : \\left[a,b\\right] \\to \\mathbb{R}<\/span> a function defined on the interval <span class=\"katex-eq\" data-katex-display=\"false\">\\left[a,b\\right]<\/span>.\nWe then say that <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> is a primitive of <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a623526 elementor-widget elementor-widget-shortcode\" data-id=\"a623526\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">In this case, <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> is the only primitive of <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> that cancels at <span class=\"katex-eq\" data-katex-display=\"false\">a<\/span>. This result is known as the fundamental theorem of analysis.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e96bb88 elementor-widget elementor-widget-shortcode\" data-id=\"e96bb88\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">So, if a function is continuous over an interval, it admits a primitive over the interval.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-01c4f44 e-flex e-con-boxed e-con\" data-id=\"01c4f44\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-24fc087 elementor-widget elementor-widget-heading\" data-id=\"24fc087\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Integral and primitive relationship \n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a6c749e elementor-widget elementor-widget-shortcode\" data-id=\"a6c749e\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Knowing a primitive of a function <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> allows you to calculate its integral over segments.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-83ea1a0 elementor-widget elementor-widget-shortcode\" data-id=\"83ea1a0\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">Indeed, if <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> is a continuous function defined on <span class=\"katex-eq\" data-katex-display=\"false\">\\left[a,b\\right]<\/span> and if <span class=\"katex-eq\" data-katex-display=\"false\">F<\/span> is a primitive of <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span>, then we have <br><span class=\"katex-eq\" data-katex-display=\"false\">\\int_{a}^{b} f(x)dx = {\\left[F(x)\\right]}_a^b = F(b) - F(a)<\/span> \n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-531d4c7 e-flex e-con-boxed e-con\" data-id=\"531d4c7\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-58dcf1a elementor-widget elementor-widget-heading\" data-id=\"58dcf1a\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Properties on primitives\n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-667f6b6 elementor-widget elementor-widget-shortcode\" data-id=\"667f6b6\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">It is possible to state a number of relationships which follow from the derivation formulae. Here we consider two derivable functions <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> and <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> defined on an interval <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span>. The table below summarises the primitives of the main operations on functions.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9808514 elementor-widget elementor-widget-image\" data-id=\"9808514\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/08\/propriete_primitive.png\" data-elementor-open-lightbox=\"yes\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MTcwNjI4LCJ1cmwiOmZhbHNlfQ%3D%3D\">\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/08\/propriete_primitive.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9c4774c elementor-hidden-desktop elementor-hidden-tablet elementor-widget elementor-widget-heading\" data-id=\"9c4774c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<span class=\"elementor-heading-title elementor-size-default\">Cliquez sur le tableau pour l'afficher en plein \u00e9cran.<\/span>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2509ce4 elementor-widget elementor-widget-shortcode\" data-id=\"2509ce4\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">You now know what a primitive is and how do you determine the primitive of a function. Primitives are mainly involved in the calculation of integrals, and are closely related to the <a href=\"\/coup-de-pouce-math-quest-ce-quune-derivee\">derivation of functions<\/a>.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-497acde elementor-widget elementor-widget-shortcode\" data-id=\"497acde\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\">If you would like to discover all the mathematical concepts involved in data science, we invite you to take a look at our courses.\n<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9413658 e-flex e-con-boxed e-con\" data-id=\"9413658\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7d0270b elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"7d0270b\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/en\/data-courses\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">Discover our training courses<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Calculating integrals is a regular part of mathematics, particularly for calculating probabilities, which is fundamental to data science. Generally, it is necessary to know a primitive of a function in order to calculate its integral. In this article, you will discover the definition of primitives and how do you determine the primitive of a function. [&hellip;]<\/p>\n","protected":false},"author":67,"featured_media":178164,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2425],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How do you determine the primitive of a function?<\/title>\n<meta name=\"description\" content=\"Calculating integrals is a regular part of mathematics, particularly for calculating probabilities, which is fundamental to data science. Generally, it is\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/en\/how-do-you-determine-the-primitive-of-a-function\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How do you determine the primitive of a function?\" \/>\n<meta property=\"og:description\" content=\"Calculating integrals is a regular part of mathematics, particularly for calculating probabilities, which is fundamental to data science. 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