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) $14.1$
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 $\int\int_D 3xy(x^2+y^2) \ dx \ dy$. Using a computer algebra system, we get $I_0 = 14.1$.

Use a Computer Algebra System to Find the Moment of Inertia