How do you integrate e^(2y)dx?

Question

bonus if you can give the solution for the following:

find the area region bounded by y=e^-x,y=1,y=2,x=2 rotated about y=2

Answer 1

If e^(2y)dx is really what you meant, then the answer is x * e^(2y). The differential is with respect to x, so all other variables are held as constants.

If you meant dy, then the answer is (1/2)e^(2y).