1. The problem statement, all variables and given/known data ∫∫[ye^(-xy)]dA R=[0,2]×[0,3] evaluate the integral. 2. Relevant equations 3. The attempt at a solution So I started with some algebra changing the integral to ∫(e^-x)[∫ye^-ydy]dx I evaluated the y portion first because its more difficult to deal with and wanted to get it out of the way. I ended up integrating by parts with: U=y dv=e^-x Dy=dy v=-e^-x and got -ye^(-y) - ∫-e^(-y)dy on the interval [0,3] and got -4e^(-3) + 1 This is now a constant, pulled it out of the x integral leaving: (-4e^(-3) +1)∫e^(-x)dx The final integral I evaluated as: -e^(-x) on [0,2] gives -e^(-2) + e^0 and this is multiplied by the previous number to give: 4e^(-6)-4e^(-3)-e^(-2)+1 Using a calculator to approximate I get a value of 0.692468 The answer in the book is .5e^(-6) + (5\2) which is approximated by a calculator as 2.5012394 I'm doing something wrong and I am wondering if there is a rule I forgot, do I need to integrate by x first and then y?