# MvCalc66

From Example Problems

Revision as of 17:14, 5 November 2012 by Keith Wasielewski (Talk | contribs)

The region of integration is a hemisphere along the positive x axis intersected by the y-z plane

In spherical co-ordinates the region is given by:

So..

By u substitution let u = cos*φ* so then du = -sin*φ* d*φ* and when *φ* = π, u = -1 and when *φ* = 0, u = 1

By half angle formula..

So..

By u substitution let u = 2*θ* so then 1/2du = d*θ* and when *θ* = π/2, u = π and when *θ* = -π/2, u = -π

Hence