How to set up a double integral with $x,y$ and $z$? Use a double integral to find the volume of the solid bounded by graphs of the equations given by: $z=xy^3, Z>0,\; X>0,\; 5X<Y<5$
How would you set up this integral? please help me. 

Here is how

$$ \int_{0}^{1}\int_{5x}^{5} xy^3 dydx.$$

You should plot the graph in xy-plane to see what's happening. 
Note: More generally, if the region bounded by two surfaces, namely from below by $z_1=f_1(x,y) $ and above by $z_2=f_2(x,y)$, then the volume of the region is given by

$$ \int\int_{A} (z_2-z_1) dA .$$

