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