Applictaion of Integration- Moment of Inertia

[electmenot]

I was wondering if my solution was correct and if I finished it all the way through.
Problem is:
Find the moment of inertia and radius of gyration of each region bounded by the given curves about the given axis.

x=1 + y^2, x=10 and y= 0 about the x-axis (rho=5)

\(\displaystyle \L\;\begin{array}{l}
I_x = \rho \int_B^A {y^2 } [f(y) - g(y)]dy \\
5\int_0^3 {y^2 } [f(0) - g(\sqrt {x - 1} )]dy \\
5\int_0^3 { - \sqrt {x - 1} } dy \\
\end{array}\)

(Hope I did the texaide right!)
Thanks for any help with this!

Edit by tkhunny: You were close.

 

[galactus]

I was wondering if my solution was correct and if I finished it all the way through.
Problem is:
Find the moment of inertia and radius of gyration of each region bounded by the given curves about the given axis.

\(\displaystyle x=1 + y^2, \;\ x=10 \;\ and \;\ y= 0\) about the x-axis (\(\displaystyle {\rho}=5\))


\(\displaystyle \L\\
\begin{array}{l}
I_x = \rho \int_B^A {y^2 } [f(y) - g(y)]dy \\
5\int_0^3 {y^2 } [f(0) - g(\sqrt {x - 1} )]dy \\
5\int_0^3 { - \sqrt {x - 1} } dy \\
\end{array}\)

(Hope I did the texaide right!)
Thanks for any help with this!

Actually, you didn't. I fix. This forum uses \(\displaystyle instead of \[.

Click on preview before submitting to make sure it's displayed correctly.\)

 

[electmenot]

thank you

Sorry about that, and Thank you for fixing it for me!