00:01
This question for the region r that's below, i want to write the double integral over the region r of fda as an iterated integral in polar coordinates.
00:10
So i'll fill in later, but what do we have? so we're going to have our function f, and when i'm in polar coordinates, da becomes rdrd theta.
00:23
So whenever you're in polar coordinates, your da becomes rdrd theta.
00:30
Now, i need to know what are my r limits of integration? well, what i imagine is radial lines coming out of the origin.
00:40
And i want to know at what r value do we enter a region and what r value do we exit our region at? so if i look at these radial lines coming out of the origin, we would enter a region when r is equal to 1.
00:56
And we would stay in a region until r was equal to 3, because these are semicircles of radii 1 and 3 respectively, centered at the origin.
01:09
So my r limits of integration are 1 and 3.
01:15
Now, what about my theta limits of integration? well, i'm looking at these radial lines coming out of the origin, and i'm going from r equals 1 to r equals 3.
01:25
And i'm doing that from theta equals where to where? well, my positive y -axis, that is theta equals pi over 2, while my negative y -axis is theta equals 3 pi over 2...