00:01
So in this question, i want to evaluate the double integral.
00:03
The double integral over r of 4 minus x squared minus y squared da, where r is the region xy, such that 0 is less than equal to x squared plus y squared, which is less than equal to 4.
00:26
So let's visualize that region.
00:28
My region is inside of the circle of radius 2 centered at the origin.
00:37
So the circle of radius 2 centered at the origin would have as its equation, x squared plus y squared equals 4, and i am looking at inside of this region.
00:51
The easiest way to do this is going to be to convert into polar coordinates.
00:56
So what can i say? well, if i have 4 minus x squared minus y squared, that can be thought of as 4 minus the quantity of x squared plus y squared.
01:13
And x squared plus y squared becomes r squared in polar coordinates.
01:18
So i'm getting a double integral of 4 minus r squared.
01:24
Now, what about my da? my da, that becomes r -d -r -d -theta.
01:32
My da becomes r -d -r -d -theta.
01:36
This time, my r's, they are extending from zero to two.
01:43
So my bars, they're going zero to two...
