00:01
Alright so we want to find the area of the region that's inside both curves.
00:05
So i've drawn them both here.
00:07
The one in green is 3 plus 2 cos theta.
00:10
The one in red is 3 plus 2 sin theta.
00:17
So this is the area we want that's inside both of these.
00:25
So the points where the two curves coincide, that tells me that sin theta equals cos theta.
00:43
You can kind of guess this from the drawing.
00:46
Theta is pi over 4 or 5 pi over 4.
00:53
So if we look at the picture, i'm going to draw a black dotted line that goes through both of our intersection points.
01:02
This line is essentially at an angle of 45 degrees.
01:07
So our total area is going to be the part between that line and the red curve and the part between the green line and the black line.
01:25
And that i can just write as the sum of two integrals.
01:31
It'll be the area for, so our area is going to be an integral from 5 pi over 4 to pi over 4.
01:49
And that is of 3 plus 2 cos theta.
02:00
That's how you find area in polar coordinates is you square the radius and then integrate on theta...