The problem is this:

Evaluate the double integral. , *D* is the triangular region with vertices (0,0), (2,4), and (6,0).

Solution Attempt:

Line 1: y=2x

Line 2: y=-x+6

0=<x=<6

Integrating ye^x dy dx yields 1/2y^2 e^x and when evaluated from 2x (bottom) to -x+6(top) it yields 1/2 e^x ((-x+6)^2 -4x^2); integrating this with respect to x yields e^x (-14+2x+x^2) and evaluating this from 0 to 6 yields -21-51e^6.

This is a problem given online and says this is incorrect but i've done this by hand and in maple. Please point out what i've done wrong. Thank you.