[Steps Shown] Consider the solid inside the surface x^2+y^2+z^2=9 and outside the surface x^2+y^2+z^2=1. Use spherical coordinates to write the integral
Question: Consider the solid inside the surface \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=9\] and outside the surface \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=1\] . Use spherical coordinates to write the integral to calculate the volume of the solid, then calculate the integral.
Deliverable: Word Document 
Solution: Show that the Jacobian for the change of variables
![[Solution] Let R be the elliptical region](/images/solutions/MC-solution-library-50549.jpg "[Solution] Let R be the elliptical region in the first quadrant")
[Solution] Let R be the elliptical region in the first quadrant
(See Solution) Integrate ∫_R∫xydA where R is the region
![[Solution] Use a change of variables to](/images/solutions/MC-solution-library-50551.jpg "[Solution] Use a change of variables to find the volume of the")
[Solution] Use a change of variables to find the volume of the
![[See Solution] Evaluate ∫_0^1∫_√y^1 sin (π x^3)dxdy](/images/solutions/MC-solution-library-50552.jpg "[See Solution] Evaluate ∫_0^1∫_√y^1 sin (π x^3)dxdy")
[See Solution] Evaluate ∫_0^1∫_√y^1 sin (π x^3)dxdy
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