Use a Computer Algebra System to Find the Moment of Inertia

Multiple Choice

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