Use cylindrical coordinates to evaluate the triple integral $$\iiint _ { E } y d V$$
where $E$ is the solid that lies between the cylinders $x ^ { 2 } + y ^ { 2 } = 3$ and $x ^ { 2 } + y ^ { 2 } = 7$ above the $x y$-plane and below the plane $z = x + 4$.
A) $8.57$
B) 0
C) $3.4$
D) $9.19$
E) $0.54$

Question

Quizplus · Accepted Answer

In cylindrical coordinates, $y = r\sin(\theta)$. The integral of $y$ over a symmetric region in the $xy$-plane from $\theta = 0$ to $2\pi$ will be zero because the positive and negative values of $y$ will cancel each other out.

Use Cylindrical Coordinates to Evaluate the Triple Integral ∭EydV\iiint _ { E } y d V∭E​ydV

Use Cylindrical Coordinates to Evaluate the Triple Integral $\iiint _ { E } y d V$