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Back to Double Integrals in Polar Coordinates

Exercise 19

Avg difficulty 2.5

Consider the iterated integral I=∫−30∫−9−y20yx2+y2+1 dx dy.I = \int_{-3}^{0} \int_{-\sqrt{9-y^2}}^{0} \frac{y}{x^2 + y^2+1} \, dx \, dy.

  1. Sketch (and label) the region of integration.

  2. Convert the given iterated integral to one in polar coordinates.

  3. Evaluate the iterated integral in (b).

  4. State one possible interpretation of the value you found in (c).

Long, Keller & Schlicker, Active Calculus Multivariable, §12.6 Double Integrals in Polar Coordinates, Exercise 19

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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.