Explanation Given : y = | 4 x − 1 | , y = x 2 − 5 , x = 0 , x = 4 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 y = | 4 x − 1 | , y = x 2 − 5 Sketching the region between the curves and interval x = 0 , x = 4 Shaded region in above graph represents the region between the curves Area between the curves is calculated as follows: A = ∫ 0 4 | | 4 x − 1 | − ( x 2 − 5 ) | d x A = ∫ 0 1 4 − 4 x + 1 − x 2 + 5 d x + ∫ 1 4 4 4 x − 1 − x 2 + 5 d x On solving above integral, A = [ − 4 x 1 + 1 1 + 1 + x − x 2 + 1 2 + 1 + 5 x ] 0 1 4 + [ 4 x 1 + 1 1 + 1 − x − x 2 + 1 2 + 1 + 5 x ] 1 4 4

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 6.1, Problem 37PS

To determine

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

y=|4x−1|,y=x2−5,x=0,x=4

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Chapter 6.1, Problem 36PS

Chapter 6.1, Problem 38PS

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3. The region between the graphs of y = x3 + 4x - 1 and y = 2x3+ 3x2 - 1

5.1: 9) Let A(x) represent the area bounded by the graph, the horizontal axis, and the vertical lines at t=0 and t=x for the graph below. Evaluate A(x)for x=1, 2, 3, and 4. A(1)=? A(2)=? A(3)=? A(4)=?

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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 y = | 4 x − 1 | , y = x 2 − 5 , x = 0 , x = 4

Solution Summary: The author calculates the area of region R between the curves, based on the following formula: lA=left[-4x1+1]

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

y=|4x−1|,y=x2−5,x=0,x=4

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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 y = | 4 x − 1 | , y = x 2 − 5 , x = 0 , x = 4

Solution Summary: The author calculates the area of region R between the curves, based on the following formula: lA=left[-4x1+1]

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Videos

To sketch the region bounded between the curves and then find the area of region between the curves y=|4x−1|,y=x2−5,x=0,x=4

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

y=|4x−1|,y=x2−5,x=0,x=4