Use a computer algebra system to find the moment of inertia $I _ { 0 }$ of the lamina that occupies the region D and has the density function $\rho ( x , y ) = 3 x y$ , if $D = \{ ( x , y ) \mid 0 \leq x \leq \pi , 0 \leq y \leq \sin ( x ) \}$ .
A) 8.313
B) 34.138
C) 24.105
D) 28.5
E) None of these

Question

Quizplus · Accepted Answer

The moment of inertia is given by the integral of the density function times the square of the distance from the point to the axis of rotation. In this case, the axis of rotation is the x-axis, so the distance from the point (x, y) to the axis of rotation is y. Therefore, the moment of inertia is given by the integral of 3xy^2 over the region D. This integral can be evaluated using a computer algebra system, and the result is 8.313.

Use a Computer Algebra System to Find the Moment of Inertia