Solve the problem.
-Find the moment of inertia about the x-axis of a thin plane of constant density $\delta = 10$ bounded by the coordinate axes and the line $\frac { x } { 2 } + \frac { y } { 8 } = 1$.
A) $\frac { 640 } { 3 }$
B) $\frac { 2560 } { 3 }$
C) $\frac { 10,240 } { 3 }$
D) $\frac { 160 } { 3 }$

Question

Quizplus · Accepted Answer

The moment of inertia about the x-axis is calculated using the integral $\int y^2 \, dA$. The region is a triangle with vertices at (0,0), (2,0), and (0,8). The moment of inertia is $\delta \int_0^2 \int_0^{8-4x} y^2 \, dy \, dx$, which evaluates to $\frac{2560}{3}$.

Solve the Problem δ=10\delta = 10δ=10 Bounded by the Coordinate Axes and the Line

Solve the Problem $\delta = 10$ Bounded by the Coordinate Axes and the Line