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Solve the given problems by integration.Find the moment of inertia with respect to the $y$ -axis of a flat plate that covers the first-quadrant region bounded by $y=e^{x^{3}}, x=1$ and the axes.

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 3

The Exponential Form

Integrals

Oregon State University

Harvey Mudd College

Idaho State University

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

03:27

Finding a moment of inerti…

01:18

Finding moments of inertia…

01:16

03:55

Determine the moment of in…

03:06

01:27

01:32

01:57

02:32

02:59

Finding a center of mass a…

problem. It is required to find the moment of inertia about ex acts off a sim plate haunted boys a problem X equal to Y minus y square and the line X plus y equals zero If the dentist e equal Tow X plus why we restored by sketching the graph So we have two equation. 1st 1 is X plus y equals to zero, which is something like that, and the thick and one ese x equal toe. Why minus why square, which is this curve cutting boy eggs at one. And if we and substitute by or sold the two questions off the car, we can get this point and why equal tow to So now he's asking about this region and we restored our solution. Boy. Completing M So am I will be equal toe integration from zeal to two and integration in wider veteran from negative y to y minus y square for our dynasty, which is X plus y. The ex knew I, which will be equal toe integration from zero to toe for Why are four over too minus two Y or three loss two way over, too. Do you want, which will be equal toe eight over 15. Now we can calculate I Iove x nursey about X x, which is digression from 0 to 2 and the fame integration in my direction. From why to why minus y square for y square and or dynasty, which is exit lous y the ex the wine. So it will be equal toe integration from 0 to 2 or wipe or six overto minus to wipe or five. Unless to Roy or four. Do you, Roy, which will be equal toe 64 over one or five. Thank you.

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