Explanation Consider the given surface bounded by the curves y = 0.25 x 4 and y = 12 − 0.25 x 4 . Find the intersect point of the above curve as follows. 12 − 0.25 x 4 = 0.25 x 4 0.5 x 4 = 12 x 4 = 12 0.5 x = 24 4 In order to find the area bounded by the curve, first draw the graph of the functions y = 0.25 x 4 and y = 12 − 0.25 x 4 as shown below in Figure 1. From the Figure 1, the vertical element is marked by dark shaded and area is bounded from 0 to 24 4 . Note that, the area of the vertical element formed by the curves y 1 = f ( x ) and y 2 = g ( x ) from a to b is A = ∫ a b ( y 2 − y 1 ) d x . Let y 1 = 0.25 x 4 and y 2 = 12 − 0.25 x 4 , then area bounded by these curves is obtained as follows. Substitute y 1 = 0.25 x 4 and y 2 = 12 − 0.25 x 4 in the mentioned note with limit of the integration from 0 to 24 4 as follows. A = 2 ∫ 0 24 4 ( 12 − 0

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

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Chapter 26.2, Problem 49E

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Chapter 26.2, Problem 48E

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