Calc
posted by Erica on .
Use integration by parts to evaluate the integral.
∫ from 1 to 4 of (√x) (ln√x) dx
Im not really sure what to choose for u and dv.
Thank you so much for the help!!

Try to set u to something that gets simpler in the derivative.
u = ln √x
du = 1/√x * 1/2√x dx = dx/2x
dv = √x
v = 2/3 x^{3/2}
∫ u dv = uv  ∫v du
= 2/3 x^{3/2} ln √x  ∫ 1/3 √x dx
= 2/3 x^{3/2} ln √x  2/9 x^{3/2}
= 2/9 x^{3/2} (3 ln √x  1)
F(4) = 16/9 (ln 8  1)
F(1) = 2/9
F(4)  F(1) = 16/9 ln 8  14/9