Post a New Question


posted by .

Evaluate the integral by changing to spherical coordinates.

The outer boundaries are from 0 to 1.
The middle one goes from -sqrt(1-x^2) to sqrt(1-x^2)
The inner one goes from -sqrt(1-x^2-z^) to sqrt(1-x^2-z^)
for 1/sqrt(x^2+y^2+z^2) dydzdx

I don't understand how to get the limits of integration. I know for rho it will be from 0 to 1. I want to know the process to get the boundaries for phi and theta since I have a few other similar problems to do.

  • Calculus -

    you are integrating over the whole sphere, so

    0 <= p <= 1 (inside-outside)
    0 <= φ <= 2π (whole x-y plane)
    0 <= θ <= π (top-to-bottom of sphere)

    There must be some examples in your text. And there are surely some online.

  • Calculus -

    The solution says the the boundary for phi is from 0 to pi as well as the one for theta.

  • Calculus -

    I'd have to think about it, but you obviously have both halves of the circle and both halves of the sphere.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

More Related Questions

Post a New Question