Evaluate using integration by parts

Rather than carrying out IBP several times, let's establish a more general result. Let

One round of IBP, setting

gives

This is called a power-reduction formula. We could try solving for explicitly, but no need. is small enough to just expand as much as we need to.

Finally,

so we end up with

and the antiderivative is

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50