Review your knowledge of the fundamental theorem of calculus and use it to solve problems.
What is the fundamental theorem of calculus?
The theorem has two versions.
We start with a continuous function f and we define a new function for the area under the curve y=f(t):
What this version of the theorem says is that the derivative of F is f. In other words, F is an antiderivative of f. Thus, the theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.
This version gives more direct instructions to finding the area under the curve y=f(x) between x=a and x=b. Simply find an antiderivative F and take F(b)−F(a).
Want to learn more about the fundamental theorem of calculus? Check out this video.