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MATH 2374 WORKSHEET

1. Describe as an elementary region: the solid bounded by x = 0, y = 0, z = 0, and
x + y + 2z = 2.
Answer: Two possibilities (there are 6 possible orderings):

or:

2. Find the volume of the solid bounded by x^2 +y^2 = 1, z = x^2 +y^2, and z = 0. You may find
it helpful to use the following integration formulas (from your book):

3. Integrate x over the pyramid with vertices (0, 0, 2), (0, 0, 0), (1, 0, 0), (0, 3, 0), and (1, 3, 0).
Answer: (other orderings may also work, I'm also showing a way to calculate this that does
not involve expanding polynomials)

4. Switch the order of integration:

Answer:

5. Switch the order of integration:

Answer:

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