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## Homework Statement

I have a question.

I have a function f(x,y,z) which is a continuous positive function in D = {(x,y,z); x^2 + y^2 +z^2<=1}. And let r = sqrt(x^2 + y^2 + z^2). I have to check whether the following jntegral is convergent.

x^2y^2z^2/r^(17/2) * f(x,y,z)dV.

## Homework Equations

Sphericak coordinates

x = rsin(a)cos(b)

y = rsin(a)sin(b)

z = rcos(a)

## The Attempt at a Solution

Because you know that f continuous and positive is can you say that the integral of f is between m and M. But now, I have to know what the other integral is. I have to use sphericak coordinates.

x = rsin(a)cos(b)

y = rsin(a)sin(b)

z = rcos(a)

The determinant is r^2sin(a). But if I calculate this with the standard boundaries:

r between 0 and R (R=1)

a between 0 and pi

b between -pi and pi

And if I take r between 1/m and 1 and let the limit m-->infinity, then I find that the integral is 8/105 pi. But the answer is 16/105 pi.

Have I do something wrong or have I need to use different boundaries?

Thank you