00:01
So in this problem, we are given the following.
00:03
We're given that x is equal to a times cosine of t.
00:08
And we're also given that y is equal to b times sine of t.
00:14
Notice that t ranges between the values of 0 and 2 pi.
00:19
And next, we want to find dx over dt.
00:24
Dx over dt is simply going to equal to negative a times sine of t.
00:28
And we also need dy over dt.
00:32
Dy over dt is going to equal to b times cosine of t.
00:39
And next, we are going to use the formula for the area bounded by the curve.
00:46
The area, let us write it here.
00:48
Area a is going to equal to 1 half times the integral along the curve c of x dy minus y dx.
01:01
So in our case, let us continue up here.
01:06
We're going to get the area to equal to 1 half times the integral from 0 to 2 pi of x dy where x is replaced with a times cosine of t times dy where dy is b times cosine of t.
01:30
And then minus in between...