Question

Find the volume bounded by the elliptic paraboloids 2 2 2 2 z x 9y and z 18 x 9y .

Answer 1

The Answer is.....

x^2+9y^2 =18-x^2-9y^2 
2x^2 + 18y^2 = 18 
x^2 + 9y^2 = 9 => 
z = 9 

part bounded by first equation: 
when x, y = 0 
z = 0 
integrate(pi*x_MAX*y_MAXdz) from 0 to 9 = 
pi * integrate(sqrt(z) * sqrt(z/9) * dz) from 0 to 9 = 
pi * integrate(z/3 * dz) from 0 to 9 = 
pi * 1/6(9^2 - 0^2) = 81/6 * pi 

part bounded by second equation: 
when x, y = 0 
z = 18 
integrate(pi*x_MAX*y_MAXdz) from 9 to 18 = 
will be the same as the first integral due to symmetry across z = 9 
answer = 2 * 81 / 6 * pi = 27pi

Hope This Helps....