Explanation Given: Consider the following equation, 4 y 2 = x and 2 y = x − 2 .............(1) Description: Area between two curves using vertical strips - If f and g are continuous on a closed interval [ a . b ] . Then the area between the two curves y = f ( x ) and y = g ( x ) is provides as, A = ∫ a b | f ( x ) − g ( x ) | d x . Area between two curves using horizontal strips - if F and G are continuous on a closed interval [ c , d ] . Then the area between the two curves x = F ( y ) and x = G ( y ) is provides as, A = ∫ c d | F ( y ) − G ( y ) | d y . Find the area bounded by the curves 4 y 2 = x and 2 y = x − 2 .. F ( y ) = 4 y 2 And G ( y ) = 2 y + 2 . So, first find where the curves interest each other means find the point of intersections. Plug the value x = 2 y + 2 from the second equation into the first equation as follow: Equate both the equations to the intersection points. 4 y 2 = 2 y + 2 4 y 2 − 2 y − 2 = 0 4 y 2 − 2 y − 2 2 y 2 − y − 1 = 0 2 y 2 − 2 y + y − 1 = 0 Further simply, 2 y ( y − 1 ) + 1 ( y − 1 ) = 0 ( y − 1 ) ( 2 y + 1 ) = 0 y = 1 , − 1 2 Use horizontal strips to find the area bounded by the curve. In the interval [ 1 , − 1 2 ] , the curve is 2 y = x − 2 on the top in the given interval x = 0

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 6, Problem 13SP

To determine

To find: The area of the regions bounded by the curves and lines in 4y2=x and 2y=x−2 .

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Chapter 6, Problem 12SP

Chapter 6, Problem 14SP

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The area of the regions bounded by the curves and lines in 4 y 2 = x and 2 y = x − 2 .

Solution Summary: The author explains how to find the area of the regions bounded by the curves and lines in 4y2 and 2y=x-2.

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To find: The area of the regions bounded by the curves and lines in 4y2=x and 2y=x−2 .

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Chapter 6 Solutions