Math 242, Fall 2013, Assignment 9

The danger already exists that the mathematicians have made a covenant with the devil to darken the spirit and to confine man in the bonds of Hell.

- Saint Augustine

Carefully define the following terms:

1. Double integral (of a function $f$ over a rectangle $R$).
2. Double Riemann sum.
3. Average value (of a function over a rectangle).
4. Iterated integral (of a function over a rectangle).

Carefully state the following theorems:

1. Properties of double integrals (equations (7) and (8) on page 836).
2. Fubini's Theorem.

Solve the following problems:

1. Section 12.1, problems 1, 3, 9, 11, and 12.
2. Section 12.2, problems 1, 3, 5, 15, 17, 19, 23, 25, 35, and 37.

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