Double Integrals II
Part 1: Iterated Double Integrals
We begin by exploring the procedure your helper application uses to evaluate iterated double integrals. You will find a discussion of this for your particular system in the worksheet.
In particular, we start with the integral of
over the region bounded above by x = y2 and below by y = x2, that is,
This is the same integral you calculated exactly and estimated with your own numerical technique in Part 3 of Double Integrals I.
- Use your helper application to compute the exact value of
- Use your helper application to compute an approximate numerical value of
Now we use your helper application to evaluate the double integral of f(x,y) = x2 + y2 over the region D bounded on the right by the circle of radius 2 centered at the origin and on the left by the line x = 1. The region D is shown in the following figure.
- Describe the line x = 1 in terms of polar coordinates r and theta.
- Write the double integral of f(x,y) = x2 + y2 over D as an iterated integral in polar coordinates.
- Use your helper application to evaluate this iterated integral exactly.
