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Exercise 24

Avg difficulty 2.5

Evaluate each of the following double or iterated integrals exactly.

  1. ∫13(∫25xy dy) dx\int_1^3 \left( \int_2^5 xy \, dy \right) \, dx

  2. ∫0π/4(∫0π/3sin⁡(x)cos⁡(y) dx) dy\int_0^{\pi/4} \left( \int_0^{\pi/3} \sin(x) \cos(y) \, dx \right) \, dy

  3. ∫01(∫01e−2x−3y dy) dx\int_0^1 \left( \int_0^1 e^{-2x - 3y} \, dy \right) \, dx

  4. ∬R2x+5y dA\iint_R \sqrt{2x + 5y} \, dA, where R=[0,2]×[0,3]R = [0,2]\times[0,3].

Long, Keller & Schlicker, Active Calculus Multivariable, §12.3 Iterated Integrals, Exercise 24

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Adapted from Active Calculus Multivariable © 2013–2026 Nicholas Long, Mitchel T. Keller, and Steven Schlicker. Licensed under CC BY-SA 4.0. Source: Active Calculus Multivariable. Imported at revision 692c03c.