Explanation Given : The graphs of x = y 3 − 26 y + 10 and x = 40 − 6 y 2 − y 3 are given as shown. Formula used : Area bounded by two curves 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 : By inspecting the signs of y 3 , we can say that the blue curve in the graph is for x = y 3 − 26 y + 10 and red curve is for x = 40 − 6 y 2 − y 3 . Also, if we look carefully, in the interval − 5 ≤ y ≤ − 1 , blue curve is to the right and when − 1 ≤ y ≤ 3 , red curve is to the right. Therefore, area bounded by the two curves is given by ∫ − 5 − 1 y 3 − 26 y + 10 – ( 40 − 6 y 2 − y 3 ) d y + ∫ − 1 3 40 − 6 y 2 − y 3 − ( y 3 − 26 y + 10 ) d y Simplifying the above expression, we get, ∫ − 5 − 1 ( y 3 − 26 y + 10 – 40 + 6 y 2 + y 3 ) d y + ∫ − 1 3 ( 40 − 6 y 2 − y 3 − y 3 + 26 y − 10 ) d y ∫ − 5 − 1 ( 2 y 3 + 6 y 2 − 26 y − 30 ) d y + ∫ − 1 3 ( 30 + 26 y − 6 y 2 − 2 y 3 ) d y Integrating above expression to get the area bounded, we get ( 2 y 4 4 + 6 y 3 3 − 26 y 2 2 − 30 y ) | − 5 − 1 + ( 30 y + 26 y 2 2 − 6 y 3 3 − 2 y 4 4 ) ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 6.1, Problem 25E

To determine

The area under two curves.

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Chapter 6.1, Problem 24E

Chapter 6.1, Problem 26E

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Chapter 6 Solutions

CALCULUS (CLOTH)

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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Prob. 48E Ch. 6.4 - Prob. 49E Ch. 6.4 - Prob. 50E Ch. 6.4 - Prob. 51E Ch. 6.4 - Prob. 52E Ch. 6.4 - Prob. 53E Ch. 6.4 - Prob. 54E Ch. 6.4 - Prob. 55E Ch. 6.4 - Prob. 56E Ch. 6.4 - Prob. 57E Ch. 6.4 - Prob. 58E Ch. 6.4 - Prob. 59E Ch. 6.4 - Prob. 60E Ch. 6.4 - Prob. 61E Ch. 6.4 - Prob. 62E Ch. 6.4 - Prob. 63E Ch. 6.4 - Prob. 64E Ch. 6.5 - Prob. 1PQ Ch. 6.5 - Prob. 2PQ Ch. 6.5 - Prob. 3PQ Ch. 6.5 - Prob. 4PQ Ch. 6.5 - Prob. 1E Ch. 6.5 - Prob. 2E Ch. 6.5 - Prob. 3E Ch. 6.5 - Prob. 4E Ch. 6.5 - Prob. 5E Ch. 6.5 - Prob. 6E Ch. 6.5 - Prob. 7E Ch. 6.5 - Prob. 8E Ch. 6.5 - Prob. 9E Ch. 6.5 - Prob. 10E Ch. 6.5 - Prob. 11E Ch. 6.5 - Prob. 12E Ch. 6.5 - Prob. 13E Ch. 6.5 - Prob. 14E Ch. 6.5 - Prob. 15E Ch. 6.5 - Prob. 16E Ch. 6.5 - Prob. 17E Ch. 6.5 - Prob. 18E Ch. 6.5 - Prob. 19E Ch. 6.5 - Prob. 20E Ch. 6.5 - Prob. 21E Ch. 6.5 - Prob. 22E Ch. 6.5 - Prob. 23E Ch. 6.5 - Prob. 24E Ch. 6.5 - Prob. 25E Ch. 6.5 - Prob. 26E Ch. 6.5 - Prob. 27E Ch. 6.5 - Prob. 28E Ch. 6.5 - Prob. 29E Ch. 6.5 - Prob. 30E Ch. 6.5 - 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Prob. 39CRE Ch. 6 - Prob. 40CRE Ch. 6 - Prob. 41CRE Ch. 6 - Prob. 42CRE Ch. 6 - Prob. 43CRE Ch. 6 - Prob. 44CRE Ch. 6 - Prob. 45CRE Ch. 6 - Prob. 46CRE Ch. 6 - Prob. 47CRE Ch. 6 - Prob. 48CRE Ch. 6 - Prob. 49CRE Ch. 6 - Prob. 50CRE Ch. 6 - Prob. 51CRE Ch. 6 - Prob. 52CRE Ch. 6 - Prob. 53CRE Ch. 6 - Prob. 54CRE

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The area under two curves.

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Chapter 6 Solutions