Question: EXAMPLE 3 Evaluate Be(x2+ y2+ z2)3/2 where B is the ball:B =(x, y, z)x2+ y2+ z24.SOLUTION Since the boundary of B is a sphere, we

EXAMPLE 3 Evaluate Be(x2+ y2+ z2)3/2 where B is the ball:B =(x, y, z)x2+ y2+ z24.SOLUTION Since the boundary of B is a sphere, we use spherical coordinates:B =(,, )02,02,0 .In addition, spherical coordinates are appropriate becausex2+ y2+ z2=2.Thus this equation givesBe(x2+ y2+ z2)3/2=02020e(2)3/22sin()d d d=0sin()d20d202e3 d=cos()0(2)13e320=43(e81) .

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