Here's the question $\int_{2}^{4}\int_{1}^{2}\int_{0}^{4}xy(z+2)dxdydz$
Is it right to distribute $xy$ to $z$ and $2$ obtaining $\int_{2}^{4}\int_{1}^{2}\int_{0}^{4}(xyz+2xy)dxdydz ?$
and then start with the inner most integral i.e $\int_{0}^{4}(xyz + 2xy)dx$ and integrate only with respect to $x$ keeping the rest constant and evaluating between $0$ and $4$. $i.e \left (\frac{x^2}{2}yz + x^2y \right )_{0}^{4}$ $=8yz + 16y $
Does the next step invlove integrating the above expression $w.r.t$ $y$ keeping $z$ constant?i.e$\int_{1}^{2}(8yz + 16y)dy$
If i follow the above step i get the final answer to be $180$ which is obviously wrong.As per the text book that i'am using it's $120$.