Evaluate the triple integral ∫∫∫_E (x)dV

Question

where E is the solid bounded by the paraboloid x=10y^2+10z^2 and x=10

Answer 1

Introduce polar coordinates in the y-z plane. You can then write the integral as:

Integral over theta from 0 to 2 pi

Integral over r from 0 to 1

Integral over x from 10 r^2 to 10

r dr dtheta dx

Answer 2

100/3*pi