Explanation Given: The integral ∬ D r − a d A Where r = x 2 + y 2 and r ≤ 1 Calculation: d A = r d r d t in polar coordinates and limits are 0 < r < 1 : 0 < t < 2 π The given integral = ∫ 0 1 ∫ 0 2 π

Calculus - Standalone book

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

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Question

Chapter 16.4, Problem 60E

To determine

$\iint_{D} r^{- a} d A$

To find:

The value of a for which the integral

$\iint_{D} r^{- a} d A$

Converge.

Where r = $\sqrt{x^{2} + y^{2}}$ and $r \leq 1$

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Check out a sample textbook solution

See solution

Chapter 16.4, Problem 59E

Chapter 16.5, Problem 1PQ

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Chapter 16 Solutions

Calculus - Standalone book

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∬ D r − a d A To find: The value of a for which the integral ∬ D r − a d A Converge. Where r = x 2 + y 2 and r ≤ 1

Solution Summary: The author explains that the integral converges if and only when a > 0 and the same rules apply for variable r.

Concept explainers

Videos

$\iint_{D} r^{- a} d A$

To find:

The value of a for which the integral

$\iint_{D} r^{- a} d A$

Converge.

Where r = $\sqrt{x^{2} + y^{2}}$ and $r \leq 1$

Want to see the full answer?

Chapter 16 Solutions

∬ D r − a d A To find: The value of a for which the integral ∬ D r − a d A Converge. Where r = x 2 + y 2 and r ≤ 1

Solution Summary: The author explains that the integral converges if and only when a > 0 and the same rules apply for variable r.

Concept explainers

Videos

∬Dr−adA To find: The value of a for which the integral ∬Dr−adA Converge. Where r =x2+y2and r≤1

Want to see the full answer?

Chapter 16 Solutions

$\iint_{D} r^{- a} d A$

To find:

The value of a for which the integral

$\iint_{D} r^{- a} d A$

Converge.

Where r = $\sqrt{x^{2} + y^{2}}$ and $r \leq 1$