Question

Find the volume (in cu units) of the solid bounded above by the surface z = f(x, y) and below by the plane region R. f(x, y) = 3x^3y; R is the region bounded by the graphs of y = x and y = x^2

Answer 1

we are given

y = x and y = x^2

we can find bounds

now, we can set up integral for volume

Firstly, we will find inner integarl

now, we can solve outer most integral

now, we can solve each integrals

and combine them

..............Answer