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 xy-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 around the z-axis, such as the region between two 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 $\iiint _ { E } y d V$