The integral of is easier to evaluate when n is odd.

(a) Evaluate(No computation allowed!)

(b) Evaluate the indefinite integral (i.e., the antiderivative) of using a simple substitution.

(c) Evaluate

(d) Differentiate the previous result to evaluate

ANSWER:

a)

Where the integrand can be written as,

Now the integral will be,

This is the integral value.

b)

The same integral can be done by substitution method also.

Let ,

Now the integral will be,

c)

As,

d)

We know that,