- #1
jonroberts74
- 189
- 0
Homework Statement
evaluate integral if R=[0,1]x[0,1]
[tex]\iint_R ln[(x+1)(y+1)]dA[/tex]
The Attempt at a Solution
[tex]\int_{0}^{1}\int_{0}^{1} ln[(x+1)(y+1)] dydx[/tex]
by parts
[tex]u=ln[(x+1)(y+1)]; du = \frac{1}{(x+1)(y+1)}dy;dv=dy;v=y[/tex]
[tex]\int_{0}^{1} \Bigg[\frac{y}{(x+1)(y+1)} - \frac{1}{x+1}\int_{0}^{1} 1 - \frac{1}{y+1}dy\Bigg]dx[/tex]
[tex]\int_{0}^{1} \Bigg[\frac{1}{2(x+1)} - \frac{1}{x+1} - \frac{ln(2)}{(x+1)}\Bigg]dx[/tex]
[tex] \frac{1}{2}ln(2) - ln(2) - ln^2(2)[/tex]
not sure what I did wrong but I know that's the incorrect answer