Question

Evaluate the triple integral:

(Integral from 0 to pi/2) (Integral from 0 to sqrt(9-y^2)) (Integral from sqrt(x^2+y^2) to sqrt(18-x^2-y^2)) (x^2 + y^2 + z^2) dzdxdy by changing to spherical coordinates.

Answer 1

Limits of y should be from 0 to a number, not 0 to pi/2. Could you upload a picture of the problem instead?

Answer 2

r = sqrt(x^2 + y^2 + z^2)

theta = arctan(y/x)

phi = arccos(z/r)

(Integral from 0 to pi/2) (Integral from 0 to sqrt(9-y^2)) (Integral from sqrt(x^2+y^2) to sqrt(18-x^2-y^2)) (x^2 + y^2 + z^2)

r = sqrt(9-y^2)

theta = arctan(y/x)

phi = arccos(z/r)by changing to spherical coordinates.