00:01
So, in this question, we have to find the centroid of the region bounded by the curve y is equal to sine 2x and y is equal to sine x where x lies in between 0 to pi over 3 or pi third.
00:25
Now, we know that we are going to give the centroid.
00:30
So, y would be equal to 1 over a say limits from a to b say half centroid f of x square minus g of x square integrate with respect to dx.
00:49
Now, plug in the values 1 over 1 over 4, 0 to pi third half then 2 sine square 2x minus 2 sine square x because we have opened it with respect to dx.
01:07
Transform this by half angle formula.
01:10
So, this is going to be limits from 0 to pi third minus cos 4x minus 1 plus cos 2x minus 1.
01:25
This is going to be equal to, place down the limits, sine 2x over 2 minus sine 4x over 4, 0 to pi third...