00:02
Hi, so we're going to be using polar coordinates to solve for this equation.
00:06
We have a da here, so this is probably our area.
00:11
That's normally what da stands for.
00:13
So we're going to be solving for the area of this equation using polar coordinates.
00:18
And we have that this object is bound in the first coordinate by y equal to zero and y equals x of x squared plus y squared equals four we could draw this quickly so we can see what it looks like so we have our twos and that would be equal to having y equal to x and our y is equal to zero because we'd have our y and we have our x so that would cover that that shows us what our portion would look like from here what we can do is we're going to use an equation so we have x squared plus y squared is equal to r squared and we have this equation here which is in the exact same format so we can set our r squared equal to four.
01:39
You know, r is equal to plus or minus two.
01:43
And because we're in the first coordinate, we know that r is going to be equal to two.
01:51
And we have y is equal to zero.
01:55
And there is an equation for, and we have y is equal to x.
02:00
And there are two more important equations that we should have.
02:02
So we have x is equal to r of, of cosine of theta and y is equal to the r of sine of theta and so from here what we're going to do is we're going to plug in for our y equals zero equation and we're going to plug into our y is equal to x equation so let's do our y is equal to zero first so if y is equal to zero we're going to have our 0 is equal to our sine theta.
02:46
So we can divide our sine theta, divide our sine theta, and we'll have zero is equal to r.
02:56
So we have our two r boundaries.
03:02
And now we're gonna be solving for our thetas.
03:04
So using our y is equal to x, we can plug in and we'll have our r boundaries.
03:12
Our sine theta is equal to our cosine theta.
03:21
And so our ours are actually gonna cross out in this case.
03:23
I'm gonna have sine theta is equal to cosine theta.
03:28
And that is true for when theta is equal to pi over four.
03:39
So we have one of our theta values.
03:42
And if we use our, our, our, over here that we had used and we have our zero is equal to our sine theta and instead we have zero is equal to sign theta.
04:00
We know this is going to be when sine is when sorry when theta is equal to zero or pi over two but because we're in the first coordinate we're going to say that theta is equal to zero...