Fundamental Theorem of Calculus

5 videos
1 skill
You get the general idea that taking a definite integral of a function is related to evaluating the antiderivative, but where did this connection come from. This tutorial focuses on the fundamental theorem of calculus which ties the ideas of integration and differentiation together. We'll explain what it is, give a proof and then show examples of taking derivatives of integrals where the Fundamental Theorem is directly applicable.

Fundamental theorem of calculus

VIDEO 8:03 minutes

Applying the fundamental theorem of calculus

VIDEO 3:54 minutes

Swapping the bounds for definite integral

VIDEO 3:00 minutes

Both bounds being a function of x

VIDEO 5:04 minutes

Proof of fundamental theorem of calculus

VIDEO 14:00 minutes

The fundamental theorem of calculus

PRACTICE PROBLEMS