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Find the indicated moment of inertia or radius of gyration.Find the radius of gyration of a plate covering the region bounded by $y^{2}=x^{3}, y=8,$ and the $y$ -axis with respect to the $y$ -axis.

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 5

Moments of Inertia

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moment of inertia. Okay. Times integral of eight months of eight minus X to the third. Exodus three halves power times X squared the act. You can expand this X squared and if you expand that you get X eight X squared minus extra 7/2 power the x. They you could evaluate the integral with the limits beings around for given the information that we have. And this gives us five 112 K over nine. The same step is going to repetition. Uh you're gonna repetitions now. So the same step same formally use the previous equations to be the exact same thing. I'm going to use again to calculate the massive object which is K. Times the integral with the same limit of eight minus X to the three have the That gives us 96 K over five. And our it's the moment of the nurses are divided by the mass and that is equal through 1.72

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