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 we 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
First switch the limits and throw a minus sign out front:
Since this needs to be 16, and f is even, must be -8.
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