Question

The acceleration of an object moving in a strange way has been modelled as a = e^x x.

A) use integration by parts to find an equation to model the velocity v if v = ∫ e^x x dx (the x is the letter x not multiplication)

B) is the problem any different if you find v = ∫ xe^x dx?

Answer 1

A) Will use equation $\int u\,dv = uv - \int v\,du$ .Into this equation v isn't a velocity.

Take $u=x,\space dv=e^x\,dx$ , then $du=dx, \space v=e^x$ .

Velocity $v =\int e^x x\,dx =x\,e^x - \int e^x\,dx =x\,e^x - e^x + C$ .

B) No, that is the same problem.