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# Divergence Integral Problem watch

1. ∫∫∫div(F) over region sphere of radius 5, in which:

F = (x^2+y^2+z^2)*(xi, yj, zk)

First of all:

div(F) = d[x(x^2+y^2+z^2)]/dx + d[y(x^2+y^2+z^2)]/dy + d[z(x^2+y^2+z^2)]/dz = 5(x^2+y^2+z^2)

Expressing in spherical coordinates:

div(F) = 5r^2

So the integral is:

∫∫∫ 5r^2 |J| dV = 5 ∫∫∫ r^4 sin(θ) drdθdφ
where the Jacobian is r^2 sin(θ)

Limits are simply:

0<r<5
0<θ<π
0<φ<

Evaluating this gave me 62500π. Answers say 100π. Help.
2. (Original post by poorform)
Straight away you have the wrong limits for r. Since r^2=x^2+y^2+z^2 and we are talking about a sphere of radius 5 then r^2=5 so r =sqrt(5).
Ah, thanx a bunch.

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Updated: March 28, 2016
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