Question

Vector Calculus:
Double integral of (x/(5+xy)^2) for x=1->2, y=0->4

Answer 1

\[\int\limits_{0}^{4}\int\limits_{1}^{2} \frac{ x }{ (5+xy)^2 } dydx\]
I know that it's easier to handle y first, but I'm not sure how to do it.

Answer 2

yes do y first because x is a constant in that.

in fact you can do each bit in your head. d/dy ( 5 + xy) ^ -1 = (-1)• ( ( 5 + xy) ^ -2 • x

you see?

Answer 3

integrate it treating y as a constant
substitute your x values in and then integrate the new function treating x as a constant

Answer 4

solve this first \[\int_{1}^{2} \frac{x}{(5+xy)^2}dy\] assuming x as a constant

Answer 5

then integrate the result with respect to x now form x=0->4

Answer 6

u sub? u=5+xy

Answer 7

yes

Answer 8

u = 5+xy
du = xdy

Answer 9

results in this?
\[\int\limits_{0}^{4} -\frac{ 1 }{ 5+x } dx\]

Answer 10

did you apply the limits correctly?

you said in the preamble: x=1->2, y=0->4

Answer 11

I switched x and y