integral from 0 to 2(integral from 0 to 1 (2x+y)^8 dx dy
My impulse is to use substitution but I am not sure if I can or not
$\displaystyle \int\limits^2_0\int\limits^1_0(2x+y)^8dxdy$ $\displaystyle =\frac{1}{2}\int\limits^2_0\left[\frac{(2x+y)^9}{9}\right]^1_0dy$ $\displaystyle =\frac{1}{18}\int\limits^2_0\left[(2+y)^9-y^9\right]dy$ $\displaystyle =\frac{1}{18}\left[\frac{(2+y)^{10}}{10}-\frac{y^{10}}{10}\right]^2_0=\ldots$ Why substitution if directly is pretty simple?
Tonio