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,