00:01
Hello students, in this question we have to find the moment of inertia along x -axis and y -axis for this shaded region.
00:08
So, for first we have to find the case of x -axis.
00:12
So, ix is equal to integral a to b y square into da.
00:20
If we consider a small element along so its area is da element.
00:28
So, we can write in this case we have da is equal to dy into dx and also dx means the distance 2 minus x.
00:43
So, we can write thus also we have y is equal to x square by 4.
00:53
So, we can write ix is equal to integral 0 to 1 as y -axis 1 inch y square da will be equal to integral 0 to 1 y square into 2 minus x is.
01:16
So, we can write x is equal to root 2 root of 4 y.
01:22
So, we have 2 root y.
01:25
So, 2 root y into dy.
01:31
So, that is equal to integral 0 to 1 2 y square minus 2 into y raise to 3 by 2 dy.
01:46
So, we can write which is equal to 2 y cube by 3 on integration minus 2 y raise to 5 by 2 divided by 5 by 2 from 0 to 1...