Question Use spherical coordinates to evaluate the triple integral III. v. ) (y – 2) dxdydz, where D is the solid region defined by the inequalities x2 + y2 + x2 0 and y > 0.
FCOEWS The Asker · Calculus
Transcribed Image Text: Use spherical coordinates to evaluate the triple integral III. v. ) (y – 2) dxdydz, where D is the solid region defined by the inequalities x2 + y2 + x2 < 4, x > 0 and y > 0.
More Transcribed Image Text: Use spherical coordinates to evaluate the triple integral III. v. ) (y – 2) dxdydz, where D is the solid region defined by the inequalities x2 + y2 + x2 < 4, x > 0 and y > 0.
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In spherical coordinates,{:[x=rho sin phi cos theta","quad y=rho sin phi sin theta","z=rho cos phi","],[dxdydz=rho^(2)sin phi d rho d phi d theta.],[x^(2)+y^(2)+z^(2) <= 4;quad x >= 0","quad y >= 0],[x >= 0","y >= 0=>0 <= theta <= (pi)/(2)],[x^(2)+y^(2)+z^(2) <= 4quad=>quadrho^(2) <= 4]:}So; quad∭(y-z)dxdydz{:[=int_(0)^(pi//2)int_(0)^(pi)int_(0)^(2)(rho sin phi sin theta-rho cos phi)rho^(2)sin phi d rho],[d phi d theta],[=int_(0)^(pi//2)int_(0)^(pi)(sin phi sin theta-cos phi)sin phi*(rho^(4))/ ... See the full answer