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Double integrals over rectangles practice problems

Iterated integrals and Fubini's theorem. 30 problems with worked solutions; in 30 of them every equation is proved by a computer algebra system.

Evaluate \( \displaystyle \iint_R x + 2 y \, dA \) where \( \displaystyle R = [0, 1] \times [0, 2] \).
Problem 11.2easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x \cos{\left(y \right)} \, dA \) where \( \displaystyle R = [0, 3] \times [0, \frac{\pi}{2}] \).
Problem 11.3easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x^{2} + y \, dA \) where \( \displaystyle R = [0, 1] \times [0, 2] \).
Problem 11.4easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R 6 x^{2} y \, dA \) where \( \displaystyle R = [0, 2] \times [0, 1] \).
Problem 11.5easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x^{2} + y \, dA \) where \( \displaystyle R = [0, 3] \times [0, 2] \).
Problem 11.6easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y \, dA \) where \( \displaystyle R = [0, 2] \times [0, 1] \).
Problem 11.7easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y \, dA \) where \( \displaystyle R = [0, 3] \times [0, 2] \).
Problem 11.8easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y^{2} \, dA \) where \( \displaystyle R = [0, 2] \times [0, 3] \).
Problem 11.9easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R 6 x^{2} y \, dA \) where \( \displaystyle R = [0, 3] \times [0, 2] \).
Problem 11.10easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y \, dA \) where \( \displaystyle R = [0, 1] \times [0, 1] \).
Problem 11.12easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x^{2} + y \, dA \) where \( \displaystyle R = [0, 3] \times [0, 1] \).
Problem 11.13easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y^{2} \, dA \) where \( \displaystyle R = [0, 1] \times [0, 3] \).
Problem 11.14easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y^{2} \, dA \) where \( \displaystyle R = [0, 3] \times [0, 2] \).
Problem 11.58easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x^{2} + y \, dA \) where \( \displaystyle R = [0, 1] \times [0, 1] \).
Problem 11.59easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x + 2 y \, dA \) where \( \displaystyle R = [0, 2] \times [0, 2] \).
Problem 11.60easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y \, dA \) where \( \displaystyle R = [0, 3] \times [0, 1] \).
Problem 11.61easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x + 2 y \, dA \) where \( \displaystyle R = [0, 1] \times [0, 3] \).
Problem 11.62easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R 6 x^{2} y \, dA \) where \( \displaystyle R = [0, 2] \times [0, 3] \).
Problem 11.63easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y \, dA \) where \( \displaystyle R = [0, 2] \times [0, 2] \).
Problem 11.64easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x^{2} + y \, dA \) where \( \displaystyle R = [0, 1] \times [0, 3] \).
Problem 11.65easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x \cos{\left(y \right)} \, dA \) where \( \displaystyle R = [0, 1] \times [0, \frac{\pi}{2}] \).
Problem 11.66easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x^{2} + y \, dA \) where \( \displaystyle R = [0, 2] \times [0, 3] \).
Problem 11.67easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x + 2 y \, dA \) where \( \displaystyle R = [0, 2] \times [0, 1] \).
Problem 11.68easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y \, dA \) where \( \displaystyle R = [0, 3] \times [0, 3] \).
Problem 11.69easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x^{2} + y \, dA \) where \( \displaystyle R = [0, 2] \times [0, 1] \).
Problem 11.70easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x \cos{\left(y \right)} \, dA \) where \( \displaystyle R = [0, 2] \times [0, \frac{\pi}{2}] \).
Problem 11.71easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R x y \, dA \) where \( \displaystyle R = [0, 1] \times [0, 2] \).
Problem 11.72easy✓ Every equation proved
Evaluate \( \displaystyle \iint_R y e^{x} \, dA \) where \( \displaystyle R = [0, 3] \times [0, 3] \).
Problem 11.1medium✓ Every equation proved
Evaluate \( \displaystyle \iint_R y e^{x} \, dA \) where \( \displaystyle R = [0, 3] \times [0, 2] \).
Problem 11.11medium✓ Every equation proved
Evaluate \( \displaystyle \iint_R y e^{x} \, dA \) where \( \displaystyle R = [0, 3] \times [0, 1] \).
Problem 11.15medium✓ Every equation proved