Explanation Given : The graphs of y = x 3 − 6 x and y = 8 − 3 x 2 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 ( U p p e r f u n c t i o n – L o w e r f u n c t i o n ) d x Calculation : By inspecting the graph carefully, we can say that the blue curve in the graph is for y = x 3 − 6 x , because it has 3 roots and red curve is for y = 8 − 3 x 2 , being an upright parabola. Also, if we look carefully, in the interval − 4 ≤ x ≤ − 1 , red curve is below the blue curve and when − 1 ≤ x ≤ 2 , red curve is above. Therefore, area bounded by the two curves is given by ∫ − 4 − 1 x 3 − 6 x – ( 8 − 3 x 2 ) d x + ∫ − 1 2 8 − 3 x 2 − ( x 3 − 6 x ) d x Simplifying the above expression, we get, ∫ − 4 − 1 ( x 3 + 3 x 2 − 6 x − 8 ) d x + ∫ − 1 2 ( 8 + 6 x − 3 x 2 − x 3 ) d x Integrating above expression to get the area bounded, we get ( x 4 4 + 3 x 3 3 − 6 x 2 2 − 8 x ) | − 4 − 1 + ( 8 x + 6 x 2 2 − 3 x 3 3 − x 4 4 ) | − 1 2 ( x 4 4 + x 3 − 3 x 2 − 8 x )...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 6.1, Problem 26E

To determine

The area under two curves.

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Chapter 6.1, Problem 25E

Chapter 6.1, Problem 27E

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Chapter 6 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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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The area under two curves.

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The area under two curves.

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Chapter 6 Solutions