Explanation When area is enclosed by two curves y = f ( x ) and y = g ( x ) area is calculated using vertical elements by subtracting the lower curve from the upper curve and evaluating the integral. Given: The curves x 2 + y 2 = 2 ----------- (i) x 2 + ( y − 1 ) 2 = 1 ------ (ii) Place the curves on X Y plane with the scale X Maximum 4 X Minimum -4 X Scale 1 Y Maximum 3 Y Minimum -3 Y Scale 1 The region OABCO is the area of enclosed between the circles (i) & (ii) Point of intersection of the curves (i) & (ii) Formula used: ( A − B ) 2 = A 2 − 2 A B + B 2 A 2 − B 2 = ( A + B ) ( A − B ) From (i), x 2 = 2 − y 2 substitute in (ii) 2 − y 2 + ( y − 1 ) 2 = 1 2 − y 2 + y 2 − 2 y + 1 = 1 3 − 2 y = 1 3 − 1 = 2 y 2 = 2 y y = 1 Put y = 1 in (i) x 2 + y 2 = 2 x 2 + 1 = 2 x 2 + 1 − 2 = 0 x 2 − 1 = 0 ( x + 1 ) ( x − 1 ) = 0 x + 1 =0; x − 1 =0 x = − 1 ; x = 1 ∴ ( − 1 , 1 ) , ( 1 , 1 ) are the points of intersection...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6.1, Problem 54E

To determine

The integral that represents the area between the circles $x^{2} + y^{2} = 2$ and $x^{2} + {(y - 1)}^{2} = 1$

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Chapter 6.1, Problem 53E

Chapter 6.1, Problem 55E

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Chapter 6 Solutions

CALCULUS (CLOTH)

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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The integral that represents the area between the circles x 2 + y 2 = 2 and x 2 + ( y − 1 ) 2 = 1

Solution Summary: The author calculates the integral that represents the area between the circles by subtracting the lower curve from the upper curve and evaluating it.

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The integral that represents the area between the circles $x^{2} + y^{2} = 2$ and $x^{2} + {(y - 1)}^{2} = 1$

Want to see the full answer?

Chapter 6 Solutions

The integral that represents the area between the circles x 2 + y 2 = 2 and x 2 + ( y − 1 ) 2 = 1

Solution Summary: The author calculates the integral that represents the area between the circles by subtracting the lower curve from the upper curve and evaluating it.

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The integral that represents the area between the circles x2+y2=2 and x2+(y−1)2=1

Want to see the full answer?

Chapter 6 Solutions

The integral that represents the area between the circles $x^{2} + y^{2} = 2$ and $x^{2} + {(y - 1)}^{2} = 1$