From the course: Complete Guide to Calculus Foundations for Data Science
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Fundamental theorem of calculus
From the course: Complete Guide to Calculus Foundations for Data Science
Fundamental theorem of calculus
- [Instructor] Everything you have learned so far has built up to what is called, the fundamental theorem of calculus. This theorem is often known as one of the most important and powerful theorems in calculus, so make sure to pay attention. Before I dive into this theorem, though, let's begin by bringing back the mean value theorem, but this time in relation to integrals. The mean value theorem for integrals states, if a function F of X is continuous over closed-bounded interval A to B, then there exists a number C, such that A less than C less than B, and F of C equals one divided by B minus A, multiplied by the integral of A to B of F of X DX. What this is stating is that there is a point C that equals the average of the function F of X. The reason it is good to know this theorem is because it is used when proving the fundamental theorem of calculus. Let's use the mean value theorem in a quick example. Let's look at the function F of X equals two plus three multiplied by X, where…
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