?The mass of a solid Q is given by \(\int_{0}^{2} \int_{0}^{\sqrt{4-x^{2}}}
Chapter 5, Problem 343(choose chapter or problem)
The mass of a solid Q is given by \(\int_{0}^{2} \int_{0}^{\sqrt{4-x^{2}}} \int_{\sqrt{x^{2}+y^{2}}}^{\sqrt{16-x^{2}-y^{2}}}\left(x^{2}+y^{2}+z^{2}\right)^{n} d z d y d x\), where n is an integer. Determine n such the mass of the solid is \((2-\sqrt{2}) \pi\).
Text Transcription:
int_0^2 int_0 ^ sqrt 4 - x^2 int_sqrt x^2 + y^2 ^ sqrt 16 - x^2 - y^2 (x^2 + y^2 + z^2)^n dz dy dx
(2 - sqrt 2) pi
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