Suppose and . Find the value of f(4).

So I first recognized that should be the antiderivative of the integral by FTC so that .

Since f(0)=0, the equation becomes:

Isolating and then taking the natural log of both sides yields: f(4)=ln11

Is that right?

My other question is this: evaluate It was a bonus question on a quiz and I'm wondering how to do it. The thing sort of looks the definition of the derivative?

The first thing I notice is that the variable in the integrand isn't with respect to x. If I rewrote it through FTC, I'd put ? I'm not really sure how to do this question. It sort of looks like it could be in the form of the definition of the derivative?