Explanation Given information: Two curves with equation y = x 3 − 6 x & y = 8 − 3 x 2 Concept and Formula Used: We have to determine which graph is on the top and then we find the point of intersection of the two curves and find the area using the formula ∫ a b [ f ( x ) − g ( x ) ] d x where f ( x ) is the top curve and g ( x ) is the bottom curve. ∫ x n d x = x n + 1 n + 1 + C Calculation: The graph of the given equation is represented by From the graphing calculator we found that the curve represented by blue is y = x 3 − 6 x And the curve represented by the red curve is y = 8 − 3 x 2 From the graph we found that x = − 4 , − 1 & 2 are point of intersections. From the graph we found that the bounded region is divided into two parts, first part from − 4 to − 1 in which y = x 3 − 6 x is at the top and y = 8 − 3 x 2 is at the bottom. And Second part from − 1 to 2 in which y = 8 − 3 x 2 is at the top and y = x 3 − 6 x is at the bottom. Therefore A = A 1 + A 2 . A 1 = ∫ a b [ f ( x ) − g ( x ) ] d x where f ( x ) = x 3 − 6 x & g ( x ) = 8 − 3 x 2 a = − 4 & b = − 1 . A 1 = ∫ − 4 − 1 [ ( x 3 − 6 x ) − ( 8 − 3 x 2 ) ] d x = ∫ − 4 − 1 [ x 3 − 6 x − 8 + 3 x 2 ] d x = [ x 4 4 ] − 4 − 1 + 3

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.1, Problem 26E

To determine

The area of the shaded region between the curves y=x3−6x&y=8−3x2.

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Chapter 6.1, Problem 25E

Chapter 6.1, Problem 27E

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Chapter 6 Solutions

Calculus - Standalone book

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 of the shaded region between the curves y = x 3 − 6 x & y = 8 − 3 x 2 .

Solution Summary: The author calculates the area of the shaded region between the two curves using a graphing calculator.

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The area of the shaded region between the curves y=x3−6x&y=8−3x2.

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Chapter 6 Solutions

The area of the shaded region between the curves y = x 3 − 6 x &amp; y = 8 − 3 x 2 .

Solution Summary: The author calculates the area of the shaded region between the two curves using a graphing calculator.

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The area of the shaded region between the curves y=x3−6x&y=8−3x2.

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Chapter 6 Solutions

The area of the shaded region between the curves y = x 3 − 6 x & y = 8 − 3 x 2 .