Use the change of variables $x = a u$ , $y = b v$ , $z = c w$ to evaluate $\iiint _ { E } y d V$ , where E is the solid enclosed by the ellipsoid $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } + \frac { z ^ { 2 } } { c ^ { 2 } } = 1$ .

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The Answer of Use the change of variables $x = a u$ , $y = b v$ , $z = c w$ to evaluate $\iiint _ { E } y d V$ , where E is the solid enclosed by the ellipsoid $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } + \frac { z ^ { 2 } } { c ^ { 2 } } = 1$ .

Use the Change of Variables x=aux = a ux=au y=bvy = b vy=bv

Use the Change of Variables $x = a u$ $y = b v$