Use integration by parts to evaluate the integral ∫ re^(r/8)dr=

Answer 1

For integration by parts: ∫udv = uv - ∫vdu

Choose u = r, and dv = e^(r/8).......then du = dr , and v = 8e^(r/8)

plug it in:

8re^(r/8) - ∫8e^(r/8)dr

8re^(r/8) - 64e^(r/8) + C

8( r - 8 ) e^(r/8) + C

To check, take the derivative of this using the product rule

Answer 2

Hi Katie,

∫udv=uv-∫vdu integration by parts relationship

If we let dv=e^r/8 and u=r

then v=8e^r/8 and du=dr

So ∫re^r/8dr=8re^r/8-8∫e^r/8dr , =8e^r/8(r-8) +c where c is a constant of integration.

Regards

Jim