Set up and evaluate a double integral required to find the moment of inertia, I, about the given line, of the lamina bounded by the graphs of the following equations. Use a computer Algebra system to evaluate the double integral. $y = 0 , y = \sqrt { x } , x = 4$, line: $x = 3$
$\rho = c x$
A) $I = \frac { 3,008 } { 513 }$
B) $I = \frac { 3,008 } { 315 }$
C) $I = \frac { 3,008 } { 315 } k$
D) $I = \frac { 315 } { 3,008 } k$
E) $I = \frac { 3,008 } { 513 } k$

Question

Quizplus · Accepted Answer

The moment of inertia about the line $x = 3$ is calculated using the double integral $\int_{0}^{4} \int_{0}^{\sqrt{x}} c x (x - 3)^2 \, dy \, dx$. Evaluating this integral gives $I = \frac{3,008}{315} k$.

Set Up and Evaluate a Double Integral Required to Find y=0,y=x,x=4y = 0 , y = \sqrt { x } , x = 4y=0,y=x​,x=4

Set Up and Evaluate a Double Integral Required to Find $y = 0 , y = \sqrt { x } , x = 4$