From the course: Complete Guide to Calculus Foundations for Data Science
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Antiderivatives
From the course: Complete Guide to Calculus Foundations for Data Science
Antiderivatives
- [Instructor] In this chapter, you will learn the third key concept of calculus, which is integrals. You'll learn what integrals are, how to define them, the differences between definite and indefinite integrals, and finally, the fundamental theorem of calculus. Let's start off with learning what anti-derivatives are. If you remember from the previous chapters, a derivative represents the rate of change of a function with respect to a variable or the slope of a tangent line. Sometimes derivatives will take your function down by a dimension. For example, if you have f of x equals x squared, the derivative of that is f prime of x equal to 2 multiplied by x. So again, it's going down from that two dimension to the one dimension. So what is an anti-derivative then? Essentially an anti-derivative is the opposite of taking a derivative, hence the prefix anti in the word. The formal definition states, for a function f of x, the anti-derivative is capital F of x, such that the capital F…
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