Evaluate $\int _ { C } x y ^ { 4 } d S$, where $C$ is the right half of the circle $x ^ { 2 } + y ^ { 2 } = 9$.
A) $293.6$
B) $292.6$
C) $291.6$
D) $295.6$
E) $294.6$

Question

Quizplus · Accepted Answer

The integral $\int _ { C } x y ^ { 4 } d S$ over the right half of the circle $x ^ { 2 } + y ^ { 2 } = 9$ evaluates to $291.6$. This is calculated by parameterizing the right half of the circle and evaluating the integral using appropriate limits.

Evaluate ∫Cxy4dS\int _ { C } x y ^ { 4 } d S∫C​xy4dS

Evaluate $\int _ { C } x y ^ { 4 } d S$