Explanation Given : The equation of parabolas y 2 = x + 5 and y 2 = 3 − x are given. Formula used : Area bounded by two curves along y -axis is calculated using the formula as given below, A r e a = ∫ a b ( C u r v e t o t h e r i g h t – C u r v e t o t h e l e f t ) d y Calculation : To plot the given equation of parabolas, we need to find point of intersection of the two curves. Symbolically, y 2 = x + 5 and y 2 = 3 − x Equating the above two equations, we get x + 5 = 3 − x 2 x = − 2 x = − 1 y = ± 2 Therefore, we are required to find the area as shown in the figure below. Area bounded by the two curves is given by ∫ − 2 2 ( ( 3 − y 2 ) − ( y 2 − 5 ) ) d y Simplifying the above expression, we get, ∫ − 2 2

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.1, Problem 29E

To determine

The area under two curves.

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Chapter 6.1, Problem 28E

Chapter 6.1, Problem 30E

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The area under two curves.

Solution Summary: The author explains how to determine the area bounded by two curves.

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The area under two curves.

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Chapter 6 Solutions