Question

Why is the Fundamental Theorem of Calculus such an incredible, fundamental theorem?

Short answer

It was such an incredible fundamental theorem, since it relates the signed area under the curves to the anti-derivatives so that we can find quickly the exact area of the curves. And it not so time consuming to find the derivative for the bigger areas.

It was used as a basic tool for calculating the definite integrals.

Step-by-step solution

Step 1. Given Information.

The Fundamental theorem of Calculus.

Step 2. Reason.

It was such an incredible fundamental theorem, since it relates the signed area under the curves to the anti-derivatives so that we can find quickly the exact area of the curves. And it not so time consuming to find the derivative for the bigger areas.

It was used as a basic tool for calculating the definite integrals.