Explanation Given : The region 0 ≤ x ≤ 1 , 0 ≤ y ≤ x 2 Calculation : Step 1: The height of the point (x, y) in the region D above the x-axis is f ( x , y ) = y Therefore, the average height is the following value: H ¯ = 1 A r e a ( D ) ∫ ∫ D y d A Step 2: We first compute the integral. The region D is vertically simple region defined by the inequalities 0 ≤ x ≤ 1 , 0 ≤ y ≤ x 2 Step 3: Therefore, ∫ ∫ D y d A = ∫ 0 1 ∫ 0 x 2 y d y d x = ∫ 0 1 1 2 y 2 | y = 0 x 2 d x = ∫ 0 1 1 2 ( x 4 − 0 ) d x = ∫ 0 1 1 2 x ...

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ISBN: 9781319050733

Author: Rogawski

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calcul…

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Chapter 16.2, Problem 54E

To determine

The average height above the x-axis of a point in the region $0 \leq x \leq 1, 0 \leq y \leq x^{2}$

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Chapter 16.2, Problem 53E

Chapter 16.2, Problem 55E

Chapter 16 Solutions

CALCULUS (CLOTH)

Ch. 16.1 - Prob. 1PQ Ch. 16.1 - Prob. 2PQ Ch. 16.1 - Prob. 3PQ Ch. 16.1 - Prob. 4PQ Ch. 16.1 - Prob. 5PQ Ch. 16.1 - Prob. 6PQ Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E

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The average height above the x-axis of a point in the region 0 ≤ x ≤ 1 , 0 ≤ y ≤ x 2

Solution Summary: The author explains how to determine the average height above the x-axis of a point in the region D.

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The average height above the x-axis of a point in the region $0 \leq x \leq 1, 0 \leq y \leq x^{2}$

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The average height above the x-axis of a point in the region 0 ≤ x ≤ 1 , 0 ≤ y ≤ x 2

Solution Summary: The author explains how to determine the average height above the x-axis of a point in the region D.

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The average height above the x-axis of a point in the region 0≤x≤1,0≤y≤x2

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Chapter 16 Solutions

The average height above the x-axis of a point in the region $0 \leq x \leq 1, 0 \leq y \leq x^{2}$