Fundamental Theorem of Calculus

Fundamental Theorem of Calculus Part-I. The First Fundamental Theorem of Calculus.

Definition:

If f is continuous on [a,b] and if F is an antiderivative of f on [a,b], then

Related Questions:

Q. Evaluate:

Solution:

Answer

It is assumed that student is well familiar with Integrating techniques.

Similarly, consider the following more general problem, which is also important for GRE Mathematics.

Q. If f is continuous on [5,2] and if F is an antiderivative of f on [5,2], where

Solution:
As we know from The First Fundamental Theorem of Calculus that

and here, just a = 2 and b = 5, so we have

Answer