Question

Use integration by parts to evaluate the definite integral.
S 12 x/sqrt of x+4 dx
0

Answer 1

I'm assuming integral from 0 to 12?

Integration by part is given by

integral of u dv = uv - integral of v du

Let u = x, dv = sqrt(x+4)^-1

Use integration to find du = dx, v = 2sqrt(x+4)

Thus, uv - int v du =

x 2 sqrt(x+4) - integral of 2 sqrt(x+4)

= 2x sqrt(x+4) - 4/3 (x+4)^(3/2)

Evaluate this from 0 to 12 to get

64/3, final answer.