Question

find:

Answer 1

\[\int\limits_{3}^{5}\int\limits_{2}^{6}\]

Answer 2

xye^(x+y) dydx

Answer 3

Hint :
\[e^{x+y} = e^x\cdot e^y\]

Answer 4

hmm, I'm assuming I'm going to have to use IBP?

Answer 5

yes it will be a trivial IBP

Answer 6

\[\int xe^x = xe^x - e^x\]

Answer 7

+C

Answer 8

Ooh, you can use separation of variables, correct?

Answer 9

and just split up the integrals in terms of only x and only y?

Answer 10

\[\int\limits_{3}^{5}\int\limits_{2}^{6} xye^{x+y}dydx = \left(\int\limits_3^5 xe^x\right)\cdot \left(\int\limits_2^6ye^ydy\right)\]

like this ?

Answer 11

yes

Answer 12

that works but still u need to use IBP

Answer 13

Okay.

Answer 14

got it. Thanks @ganeshie8