Solve the problem.
-Find the moment of inertia about the $x$-axis of a thin triangular plate bounded by the coordinate axes and the line $x + y = 6$ if $\delta ( x , y ) = x + y$.
A) $\frac { 7776 } { 5 }$
B) $\frac { 3888 } { 5 }$
C) $\frac { 2592 } { 5 }$
D) 864

Question

Quizplus · Accepted Answer

The moment of inertia about the x-axis is calculated using the integral $\int \int y^2 \delta(x,y) \, dA$. For the given triangle, the limits are from 0 to 6 for x and 0 to $6-x$ for y. Solving the integral with $\delta(x,y) = x+y$ gives $\frac{2592}{5}$.

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