Demonstrate the second Fundamental Theorem of calculus by differentiating the result

Question

(a) integrate to find F as a function of x and (b) demonstrate the second Fundamental Theorem of calculus by differentiating the result in part (a) .

Answer 1

Step 1:

(a)

The function is .

Power rule of integrals :  .

Step 2:

(b)

Second fundamental theorem of calculus :

If the function is continuous on the interval then

Here

.

Solution:

(a)

(b)