help on integral iteration.?

Question

∫∫ xye^(-x^(2)*y) R= {(x,y,) : 0 <= x <= 1 , 0 <= y <= 2}

I'm gettting - (1+e^2)/e^2

Please help.

Answer 1

I'm not sure if your answer is + or -, it should be +. Also, there is a factor of 1/2 for the whole thing.

Answer 2

Integrate with respect to x first to get
∫-(1/2)[e^(-y) - 1] dy, y from 0 to 2
= -(1/2)[-e^(-2) +1 - 2]
= (1/2)(1+e^2)/e^2

Answer 3

separable integral

∫ y dy * ∫ xe^(-x^(2)) dx=?


y^2/2 for y=0 to 2 gives 2-0=2

∫ xe^(-x^(2)) dx
=(-e^(-x^2))/2
for x=0 to 1
gives -1/(2e)-(1/2)
hence the answer will be the product
2* (-1/(2e)-(1/2))=
-1/e-1