Mathematics 241 – Multivariable Calculus Quiz 9 – December 10, 2010

Your Name:

A. (10) Set up (but do not evaluate) the triple integral of f(x, y, z) = y over the hemisphere H = {(x, y, z) | x^{2} + y^{2} + z^{2} ≤ 25, y ≥ 0} using spherical coordinates.

B. (10) Evaluate the line integral ∫_{α} F · T ds where α is the unit circle centered at (0, 0), traversed counterclockwise, and F (x, y) = (−x, y + x). Any legal method is OK.