Integration By Parts Problem
During a surge in the demand for electricity, the rate, r, at which energy is used can be approximated by the following function where t is the time in hours and b is a positive constant.
a.) (a) Find the total energy, E, used in the first T hours. Give your answer as a function of b.
So I know that I want the integral of r(t) from 0 to T. I tried to find the integral and got:
Is this right?
And also, I have NO IDEA what it means when the question says that it wants the answer in terms of b. "b" is a constant! How do you do that?! Is that like E(b), and if so, what would that look like?