Evaluating the Double Integral of F(bar) in C

[andyk23]

$\int$ xy^3 dx+ x^5 dy, where C is the rectangle with vertices (0,0), (4,0), (4,2), and (0,2)

F(bar)= <P,Q> <xy^3, x^5>
derivative of P with respect to y= 3xy^2
derivative of Q with respect to x= 5x^4
Double $\int$ (5x^4-3xy^2) dx dy with limits for x from (0,2) and y limits (0,4)
I get 0 for the answer but that is incorrect. I feel like I'm making a small error somewhere. Any guidance would be helpful, thanks.

 

[Dick]

Looks to me like you've got your x and y limits reversed.