00:01
Let us consider the figure here this circle is of radius r equal to 1 and the centroid is of the equation r equals to 1 times 1 plus cos theta.
00:23
So now we need to find the area between this circle and this centroid which is the shaded region.
00:32
Now let us first find the angle between the center of the circle and the point of intersection of the cardio.
00:42
So here in order to find the angle, let is equate these two equations.
00:47
So we have 1 plus cos theta equals to 1.
00:51
Therefore, cos theta is equal to 1 minus 1 equals to 0.
00:55
That will imply that theta is equal to 5 by 2.
00:59
And from the figure itself, we can identify the answer.
01:03
Angle between the center of the circle to the point of intersection of the cardio and the circle, which is 90 degrees.
01:11
Now let us find the area.
01:15
So we have the area equals to here we will find the area of the upper part of the x -axis and multiply it with 2 to get the total area of the shaded region.
01:29
So we have two times of integral.
01:31
The angle is from 0 to pi by 2.
01:33
So we have 0 to pi by 2.
01:34
So we have 0 to pi by 2...