The triple integral using the spherical coordinates is 16 π .
Given :
Use spherical coordinates. Evaluate( x^2 + y^2 + z^2 )^1/2 dv, where B is the ball with center the origin and radius 3.
we know that ,
= ∫∫∫ ( x^2 + y^2 + z^2 )^1/2 dv
= ∫∫∫ x . x^2 .sin Φ dΦ dθ dx
where lower limits and upper limits are ( 0 , 2 ) , ( 0 , 2 π ) , ( 0 , π ) .
= ∫ x^3 . dx ∫ dθ ∫ sin Φ dΦ
= 2^4 / 4 * 2 π * 2
= 4 * 2 π * 2
= 8 π * 2
= 16 π
Learn more about the coordinates here:
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