Question Use spherical coordinates to evaluate the triple integral (z2 – y) dxdydz, where D is the solid region defined by the inequalities x2 + y2 + x2 0 and z > 0.

WA3B7I The Asker · Advanced Mathematics

Transcribed Image Text: Use spherical coordinates to evaluate the triple integral (z2 – y) dxdydz, where D is the solid region defined by the inequalities x2 + y2 + x2 < 4, y> 0 and z > 0.
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Transcribed Image Text: Use spherical coordinates to evaluate the triple integral (z2 – y) dxdydz, where D is the solid region defined by the inequalities x2 + y2 + x2 < 4, y> 0 and z > 0.
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D1D9HA

spherical coordinate{:[x=rho sin phi cos theta],[y=rho sin phi sin theta],[z=rho cos phi],[rho^(2)=x^(2)+y^(2)+z^(2)],[dxdydz=rho^(2)sin phi d rho d theta d phi],[I=∭(x^(2)-y)dxdydz],[I=∭(rho^(2)cos^(2)phi-rho sin phi sin theta)rho^(2)sin phi d rho d theta d phi],[" Clearly "quad0 <= rho <= 2],[0 <= theta <= (pi)/()rarr" Nole this angle ... See the full answer