TABLE OF CONTENTS

Find given that

Pull out the constant from the integral to get

We're trying to find , which means we need to get that all by itself on one side of the equation. Divide both sides by 2, and there you are:

Split up the integral:

We know , so

Combine the tricks used in the previous two examples to find

given that

Split up the integral and pull out the constant 5 from the second term:

We know

so we can put that in to get

Since , it's time to solve:

Find assuming that f is even and that

Since f is even,

Since this needs to be 16, must be 8.

Switch the limits, switch the signs:

Since f is even, this equals

So

which means .

Whenever you're dealing with an odd function, you want to be on the lookout for integrals of the form ,because you know that's equal to 0.