# 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**