Explanation Given : x − a x i s , y = x 3 − 2 x 2 − x + 2 Formula Used: The area of region R between the curves defined by curves y = f ( x ) and y = g ( x ) from x = a to x = b is calculated by subtracting the area between the lower curve and x-axis from the area between the upper curve and x-axis A = ∫ a b | f ( x ) − g ( x ) | d x Calculation: Curves are given as x − a x i s , y = x 3 − 2 x 2 − x + 2 Thus, curves as y = x 3 − 2 x 2 − x + 2 y = 0 First find the intersection points of two curves by equating the curves x 3 − 2 x 2 − x + 2 = 0 ( x − 2 ) ( x + 1 ( x − 1 ) ) = 0 x = − 1 , 1 , 2 Sketching the region between the curves and interval x = − 1 , x = 1 , x = 2 Shaded region in above graph represents the region between the curves Area between the curves is calculated as follows: A = ∫ − 1 2 | x 3 − 2 x 2 − x + 2 | d x A = ∫ − 1 1 x 3 − 2 x 2 − x + 2 d x + ∫ 1 2 − x 3 + 2 x 2 + x − 2 d x On solving above integral, A = [ x 3 + 1 3 + 1 − 2 x 2 + 1 2 + 1 − x 1 + 1 1 + 1 + 2 x ] − 1 1 + [ − x 3 + 1 3 + 1 + 2 x 2 + 1 2 + 1 + x 1 + 1 1 + 1 − 2 x ] 1 2

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.1, Problem 41PS

To determine

To sketch the region bounded between the curves and then find the area of region between the curves

x−axis,y=x3−2x2−x+2

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Chapter 6.1, Problem 40PS

Chapter 6.1, Problem 42PS

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Chapter 6 Solutions

Calculus

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To sketch the region bounded between the curves and then find the area of region between the curves x − a x i s , y = x 3 − 2 x 2 − x + 2

Solution Summary: The author calculates the area of region R between two curves by subtracting the intersection points of the curve and equating them.

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To sketch the region bounded between the curves and then find the area of region between the curves

x−axis,y=x3−2x2−x+2

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Chapter 6 Solutions

To sketch the region bounded between the curves and then find the area of region between the curves x − a x i s , y = x 3 − 2 x 2 − x + 2

Solution Summary: The author calculates the area of region R between two curves by subtracting the intersection points of the curve and equating them.

Concept explainers

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To sketch the region bounded between the curves and then find the area of region between the curves x−axis,y=x3−2x2−x+2

Want to see the full answer?

Chapter 6 Solutions

To sketch the region bounded between the curves and then find the area of region between the curves

x−axis,y=x3−2x2−x+2