Explanation Given information : Given graph of a parabola having its axis as y axis, is opening down. Thus, on getting standard equation of such parabola with given points on it, its equation is found as: x 2 = − 1 2 ( y − 2 ) ⇒ 2 x 2 = − y + 2 ⇒ y = 2 ( 1 − x 2 ) ... ( i ) Further, required shaded area ABC is obtained when the bounded area region OBC between above parabola, x axis and y axis is doubled as this region is symmetric about vertical y axis. Accordingly it is also given from the given graph that for the region OBC lower limit a = 0 and upper limit b = 1 . Formula used : Such shaded area can be calculated using integral calculus where this area Aof region OBC, is calculated using the following integration formula: A = ∫ a b y d x Where a is the x coordinate of starting point of shaded area and b is the x coordinate of end point of shaded area, on the curve of parabola

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 1.1, Problem 46PS

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To calculate the shaded area enclosed by the curve of different functions as shown in below figure:

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Chapter 1.1, Problem 45PS

Chapter 1.1, Problem 47PS

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Chapter 1 Solutions

Calculus

Ch. 1.1 - Prob. 1PS Ch. 1.1 - Prob. 2PS Ch. 1.1 - Prob. 3PS Ch. 1.1 - Prob. 4PS Ch. 1.1 - Prob. 5PS Ch. 1.1 - Prob. 6PS Ch. 1.1 - Prob. 7PS Ch. 1.1 - Prob. 8PS Ch. 1.1 - Prob. 9PS Ch. 1.1 - Prob. 10PS

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To calculate the shaded area enclosed by the curve of different functions as shown in below figure:

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To calculate the shaded area enclosed by the curve of different functions as shown in below figure:

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Chapter 1 Solutions