{"id":178162,"date":"2024-02-28T14:58:08","date_gmt":"2024-02-28T13:58:08","guid":{"rendered":"https:\/\/liora.io\/en\/?p=178162"},"modified":"2026-08-09T19:38:45","modified_gmt":"2026-08-09T18:38:45","slug":"how-do-you-determine-the-primitive-of-a-function","status":"publish","type":"post","link":"https:\/\/liora.io\/en\/how-do-you-determine-the-primitive-of-a-function","title":{"rendered":"How do you determine the primitive of a function?"},"content":{"rendered":"\n

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<\/strong><\/p>\n\n\n

What is the primitive of a function and how do you determine the primitive of a function?<\/h2>\n\n\n

Let [a,b]<\/span> be an interval, and f : [a,b] \u2192 \u211d<\/span> a function defined on the interval [a,b]<\/span>. We say that f<\/span> admits a primitive on [a,b]<\/span> if there exists a differentiable function F : [a,b]\u2192 \u211d<\/span> such that for any x in ]a,b[<\/span>, F\u2032<\/sup>(x) = f(x)<\/span>. \nWe then say that F<\/span> is a primitive of f<\/span>.\nFor example, for f(x) = 3 x2<\/sup> + 5<\/span>, a primitive of f<\/span> on \u211d<\/span> is F(x) = x3<\/sup> + 5 x<\/span>. This can be verified by deriving F<\/span>.\nWe then say that F<\/span> is a primitive of f<\/span>.\nThe following table shows the primitives of some common functions.\nWe then say that F<\/span> is a primitive of f<\/span>.<\/p>\n\n\n

\n\"Illustration <\/a><\/figure>\n\n\n

Cliquez sur le tableau pour l’afficher en plein \u00e9cran.<\/p>\n\n\n

Sufficient condition for the existence of a primitive\n<\/h2>\n\n\n

Let [a,b]<\/span> be an interval, and f : [a,b] \u2192 \u211d<\/span> a function defined on the interval [a,b]<\/span>.\nWe then say that F<\/span> is a primitive of f<\/span>.\nLet [a,b]<\/span> be an interval, and f : [a,b] \u2192 \u211d<\/span> a function defined on the interval [a,b]<\/span>.\nWe then say that F<\/span> is a primitive of f<\/span>.\nIn this case, F<\/span> is the only primitive of f<\/span> that cancels at a<\/span>. This result is known as the fundamental theorem of analysis.\nSo, if a function is continuous over an interval, it admits a primitive over the interval.<\/p>\n\n\n

Integral and primitive relationship \n<\/h2>\n\n\n

Knowing a primitive of a function f<\/span> allows you to calculate its integral over segments.\nIndeed, if f<\/span> is a continuous function defined on [a,b]<\/span> and if F<\/span> is a primitive of f<\/span>, then we have \u222ba<\/sub>b<\/sup> f(x)dx = {[F(x)]}a<\/sub>b<\/sup> = F(b) \u2212 F(a)<\/span><\/p>\n\n\n

Properties on primitives\n<\/h2>\n\n\n

It is possible to state a number of relationships which follow from the derivation formulae. Here we consider two derivable functions f<\/span> and g<\/span> defined on an interval I<\/span>. The table below summarises the primitives of the main operations on functions.<\/p>\n\n\n

\n\"Illustration <\/a><\/figure>\n\n\n

Cliquez sur le tableau pour l’afficher en plein \u00e9cran.\t\t\n\t\tYou 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 derivation of functions<\/a>.\nIf you would like to discover all the mathematical concepts involved in data science, we invite you to take a look at our courses.<\/p>\n\n\n

Discover our training courses<\/a><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"

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. […]<\/p>\n","protected":false},"author":76,"featured_media":178164,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[2433],"class_list":["post-178162","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-data-ai"],"acf":[],"_links":{"self":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts\/178162","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/users\/76"}],"replies":[{"embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/comments?post=178162"}],"version-history":[{"count":3,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts\/178162\/revisions"}],"predecessor-version":[{"id":211002,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/posts\/178162\/revisions\/211002"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/media\/178164"}],"wp:attachment":[{"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/media?parent=178162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/liora.io\/en\/wp-json\/wp\/v2\/categories?post=178162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}