Charge over a triangular region

[unknown_2]

Homework Statement

-Given that $$\rho_{v}$$=6xy C/$$m^{2}$$, Calculate the total charge on the triangular region.

-the verticies of the triangle are: (0,0), (2,2) and (4,0)

Homework Equations

$$Q=\int_{s}\rho_{v}ds$$

The Attempt at a Solution

$$=\int^{4}_{0}\int^{-x+4}_{x}6xy dydx$$
$$=\int^{4}_{0}48x - 24x^{2} dx$$
$$=24x^{2}-8x^{3}|^{4}_{0}$$
$$=-128C$$

According to the textbook the correct answer is 32C

any help would be appreciated!
Thanks,

 

[kuruman]

You got your integration limits mixed up. The maximum value for x is 2 m. Draw a picture and you will see why.