Explanation Given: The provided equations are: y = x , y = 2 x + 2 , x = 0 and x = 4 Formula used: The area of a region is given by A = ∫ x l x h ∫ y l y h d y d x Use the integration formula ∫ x n d x = x n + 1 n + 1 Calculation: The equation x = 0 represents y -axis. The equation x = 4 is a perpendicular on x -axis at 4. The equation y = x is a straight-line pass through origin. To plot y = 2 x + 2 convert it in intercept form y = 2 x + 2 − 2 x + y = 2 − 2 x + y 2 = 2 2 − x + y 2 = 1 Intercept at x -axis is -1 and intercept at y -axisis 2. Find intersection point of y = x and y = 2 x + 2 x = 2 x + 2 x = − 2 Put the obtained x = − 2 in y = x . This gives y = − 2 Intersection point is ( − 2 , 2 ) . Intersection point of y = x and x = 4 is ( 4 , 4 )

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ISBN: 9780100453777

Author: Larson

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Chapter 14, Problem 9RE

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To calculate: The area of the region bounded by the graphs of given equation y=x, y=2x+2, x=0 and x=4.

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Chapter 14, Problem 8RE

Chapter 14, Problem 10RE

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Chapter 14 Solutions

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The area of the region bounded by the graphs of given equation y = x , y = 2 x + 2 , x = 0 and x = 4 .

Solution Summary: The author calculates the area of a region bounded by the graphs of given equations y=x,

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To calculate: The area of the region bounded by the graphs of given equation y=x, y=2x+2, x=0 and x=4.

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Chapter 14 Solutions