Problems

Use an appropriate change of coordinates to evaluate the following integrals:

Problem


Underscript[∫∫, D]x ydA where D is the region between the graphs of:
    y=(2 - 2x^2)^(1/3), x^2=3-y^3/2, y^3=2x-1, and x=4+y^3/2for x≥0.

Problem

Underscript[∫∫∫, D]x(y^2+z^2)dV where D is the region between the graphs of:
    3≤y^2+2y+4z^2≤8, -x +2y+3z=15  and  x=y^2-3z^2
    
(Kindly hint:  The coordinate system here is given by the first compound inequality.)


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