Let

R

be a region in the

xy

-plane that is bounded by a piecewise smooth simple closed curve

C

and suppose that the moments of inertia of

R

about the

x

-and

y

-a

I_(x)

and

I_(y)

. Evaluate the following integral in terms of

I_(x)

and

I_(y)

\

o\\\\int_C grad(r^(4))*nds

where

r=\\\\sqrt(3x^(2)+2y^(2))

\

o\\\\int_C grad(r^(4))*nds=

Let R be a region in the xy-plane that is bounded by a piecewise smooth simple closed curve C and suppose that the moments of inertia of R about the x - and y-a Ix and Iy. Evaluate the following integral in terms of Ix and Iy c(r4)n ds where r=3x2+2y2 C(r4)nds= Let R be a region in the xy-plane that is bounded by a piecewise smooth simple closed curve C and suppose that the moments of inertia of R about the x - and y-a Ix and Iy. Evaluate the following integral in terms of Ix and Iy c(r4)n ds where r=3x2+2y2 C(r4)nds=