Explanation Given : f ( x , y ) = ( x 2 + y 2 ) − 2 ,The inequalities ( x 2 + y 2 ) ≤ 2 , x ≥ 1 Formula Used : Change of Variables Calculation : Step 1: The region D lies in the angular sector − π 4 ≤ θ ≤ π 4 Step 2: The vertical line x = 1 has polar equation r c o s θ = 1 or r = s e c θ . The circle x 2 + y 2 = 2 has polar equation r = 2 . Therefore, D has the following description: − π 4 ≤ θ ≤ π 4 , sec θ ≤ r ≤ 2 The function in polar coordinates is f ( x , y ) = ( x 2 + y 2 ) − 2 = ( r 2 ) − 2 = r − 4 Step 3: Using change of variables we obtain ∬ D ( x 2 + y 2 ) − 2 d A = >&#...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.4, Problem 15E

To determine

To calculate : The value of the integral of $f (x, y) = {(x^{2} + y^{2})}^{- 2}$ over the region given by the inequalities $(x^{2} + y^{2}) \leq 2, x \geq 1$ by changing to polar coordinates.

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Chapter 16.4, Problem 14E

Chapter 16.4, Problem 16E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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The value of the integral of f ( x , y ) = ( x 2 + y 2 ) − 2 over the region given by the inequalities ( x 2 + y 2 ) ≤ 2 , x ≥ 1 by changing to polar coordinates.

Solution Summary: The author explains how to calculate the integral of f (x, y) over the region given by the inequalities by changing to polar coordinates.

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To calculate : The value of the integral of $f (x, y) = {(x^{2} + y^{2})}^{- 2}$ over the region given by the inequalities $(x^{2} + y^{2}) \leq 2, x \geq 1$ by changing to polar coordinates.

Want to see the full answer?

Chapter 16 Solutions

The value of the integral of f ( x , y ) = ( x 2 + y 2 ) − 2 over the region given by the inequalities ( x 2 + y 2 ) ≤ 2 , x ≥ 1 by changing to polar coordinates.

Solution Summary: The author explains how to calculate the integral of f (x, y) over the region given by the inequalities by changing to polar coordinates.

Videos

To calculate : The value of the integral of f(x,y)=(x2+y2)−2 over the region given by the inequalities (x2+y2)≤2,x≥1 by changing to polar coordinates.

Want to see the full answer?

Chapter 16 Solutions

To calculate : The value of the integral of $f (x, y) = {(x^{2} + y^{2})}^{- 2}$ over the region given by the inequalities $(x^{2} + y^{2}) \leq 2, x \geq 1$ by changing to polar coordinates.