Explanation Given : Region bounded by y = x 2 and y = x + 2 , Integral f ( x , y ) = x Calculation : Step 1: The domain D is the shaded region in the figure Step 2: To find the inequalities defining the domain D as a vertically simple region, we must first find the x-coordinates of the two points where the line y = x + 2 and the parabola y = x 2 intersect. That is x + 2 = x 2 ⇒ x 2 − x − 2 = ( x − 2 ) ( x + 1 ) = 0 ⇒ x 1 = − 1 , x 2 = 2 Step 3: We describe the domain by the following inequalities: − 1 ≤ x ≤ 2 , x 2 ≤ y ≤ x + 2

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.2, Problem 9E

To determine

The value of the integral $f (x, y) = x$ over the region bounded by $y = x^{2}$ and $y = x + 2$ .

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Chapter 16.2, Problem 8E

Chapter 16.2, Problem 10E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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The value of the integral f ( x , y ) = x over the region bounded by y = x 2 and y = x + 2 .

Solution Summary: The author explains how to determine the value of the integral f (x, y) = x over the vertically simple region D.

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The value of the integral $f (x, y) = x$ over the region bounded by $y = x^{2}$ and $y = x + 2$ .

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Chapter 16 Solutions

The value of the integral f ( x , y ) = x over the region bounded by y = x 2 and y = x + 2 .

Solution Summary: The author explains how to determine the value of the integral f (x, y) = x over the vertically simple region D.

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The value of the integral f(x,y)=x over the region bounded by y=x2 and y=x+2.

Want to see the full answer?

Chapter 16 Solutions

The value of the integral $f (x, y) = x$ over the region bounded by $y = x^{2}$ and $y = x + 2$ .