Question

express the integral e f(x, y, z) dv as an iterated integral in six different ways, where e is the solid bounded by the given surfaces. y

Answer 1

To express the integral e f(x, y, z) dv as an iterated integral in six different ways, you can rearrange the order of integration with respect to x, y, and z. Here are six different possibilities: dx dy dz, dy dx dz, dy dz dx, dz dy dx, dz dx dy, dx dz dy. Each of these different orders of integration will give you a different iterated integral for the given solid bounded by the surfaces.

Step-by-step explanation:

To express the integral e f(x, y, z) dv as an iterated integral in six different ways, you can rearrange the order of integration with respect to x, y, and z. Here are six different possibilities:

1. dx dy dz: Integrate first with respect to x, then y, and finally z.
2. dy dx dz: Integrate first with respect to y, then x, and finally z.
3. dy dz dx: Integrate first with respect to y, then z, and finally x.
4. dz dy dx: Integrate first with respect to z, then y, and finally x.
5. dz dx dy: Integrate first with respect to z, then x, and finally y.
6. dx dz dy: Integrate first with respect to x, then z, and finally y.

Each of these different orders of integration will give you a different iterated integral for the given solid bounded by the surfaces.