Evaluate Double integral over triangular region

[nlsherrill]

Homework Statement

Evaluate the double integral.

[I don't know how to write it in latex, sorry, but its the double integral over the region 'd' of ye^x dA

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

Homework Equations

The Attempt at a Solution

So the limits of integration I have are .5y to 6-y with respect to x, and 0 to 4 with respect to y. I think this is right. The farthest I can get is:

Integral 0..4 ye^6-y - ye^.5y dy

I can't figure out how to integrate these terms. Any hints?

 

[Mark44]

Homework Statement

Evaluate the double integral.

[I don't know how to write it in latex, sorry, but its the double integral over the region 'd' of ye^x dA

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

Homework Equations

The Attempt at a Solution

So the limits of integration I have are .5y to 6-y with respect to x, and 0 to 4 with respect to y. I think this is right. The farthest I can get is:

Integral 0..4 ye^6-y - ye^.5y dy

I can't figure out how to integrate these terms. Any hints?

Here's your integral in LaTeX:
$$\int_{y = 0}^4 (ye^{6 - y} - ye^{y/2})dy$$

Break this up into two integrals. Note that e^{6 - y} = e⁶e^-y

Integration by parts should work on both integrals.

 

[nlsherrill]

Thanks! forgot about integration by parts.