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

The integral of $y$ over a symmetric region about the $z$-axis, such as between two concentric cylinders, is zero because the positive and negative contributions of $y$ cancel 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 $\iiint _ { E } y d V$