Solve the triple integral(spherical coordinates can be used) (outter)Integral(fr

Question

Solve the triple integral(spherical coordinates can be used) (outter)Integral(from 0 to 4) Integral(from 0 to sqrt(16-z^2)) (inner)Integral (from 0 to sqrt(16-y^2-z^2)) dx dy dz Need a worked out solution. Answer should be (32pi)/3. Only solutions that yield answer above please

Explanation / Answer

FOLLOW THIS Use spherical coordinates. x^2 + y^2 + z^2 = 16 ==> ? = 4. y = ?(x^2 + y^2) ==> ? cos ? = ? sin ? ==> ? = ?/4. Hence, the volume ??? 1 dV equals ?(? = 0 to 2?) ?(? = 0 to ?/4) ?(? = 0 to 4) 1 * (?^2 sin ? d? d? d?) = 2? ?(? = 0 to ?/4) sin ? d? * ?(? = 0 to 4) ?^2 d? = 2? * (-cos ?) {for ? = 0 to ?/4} * (1/3)?^3 {for ? = 0 to 4} = 2? * (1 - ?2/2) * (64/3) = (64?/3) * (2 - ?2).

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