Explanation Given : x = 8 − y 2 , x = y 2 Formula Used: The area of region R between the curves defined by curves y = f ( x ) and y = g ( x ) from x = a to x = b is calculated by subtracting the area between the lower curve and x-axis from the area between the upper curve and x-axis A = ∫ a b | f ( x ) − g ( x ) | d x Calculation: Curves are given as x = 8 − y 2 , x = y 2 First curve is given as x = 8 − y 2 y 2 = 8 − x y = 8 − x , − 8 − x Now, second curve is given as x = y 2 y 2 = x y = x , − x In order to find the intersection of the two curves, let us equate both the curves Equating 8 − x = − 8 − x 8 − x = − 8 − x 2 8 − x = 0 4 ( 8 − x ) = 0 x = 8 Equating x = − x x = − x 2 x = 0 x = 0 Equating 8 − x = x 8 − x = x 8 − x = x 2 x = 8 x = 4 Equating 8 − x = − x 8 − x = − x 8 − x = x 2 x = 8 x = 4 Putting x = 4 in 8 − x = − x 8 − x = − x 8 − 4 = − 4 4 ≠ − 4 Hence, no solution

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.1, Problem 30PS

To determine

To sketch the region bounded between the curves and then find the area of region between the curves

x=8−y2,x=y2

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Chapter 6.1, Problem 29PS

Chapter 6.1, Problem 31PS

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To sketch the region bounded between the curves and then find the area of region between the curves x = 8 − y 2 , x = y 2

Solution Summary: The author explains how to sketch the region bounded between the curves and find the area of region between them.

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To sketch the region bounded between the curves and then find the area of region between the curves

x=8−y2,x=y2

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To sketch the region bounded between the curves and then find the area of region between the curves x = 8 − y 2 , x = y 2

Solution Summary: The author explains how to sketch the region bounded between the curves and find the area of region between them.

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To sketch the region bounded between the curves and then find the area of region between the curves x=8−y2,x=y2

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Chapter 6 Solutions

To sketch the region bounded between the curves and then find the area of region between the curves

x=8−y2,x=y2