Explanation Given : The linear function f ( x , y ) = m x + n y + p , the ellipse x 2 a 2 + y 2 b 2 ≤ 1 Calculation : Step 1: The average value of the linear function f ( x , y ) = m x + n y + p over the ellipse D is f ¯ = 1 A r e a ( D ) ∫ ∫ D f ( x , y ) d A = 1 A r e a ( D ) ∫ ∫ D ( m x + n y + p ) d A = m . 1 A r e a ( D ) ∫ ∫ D x d A ︸ I 1 + n . 1 A r e a ( D ) ∫ ∫ D y d A ︸ I 21 + 1 A r e a ( D ) ∫ ∫ D p d A Step 2: I 1 and I 2 are the average values of the x-coordinates and y-coordinates of a point in the region enclosed by the ellipse...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.2, Problem 57E

To determine

The average value of the linear function $f (x, y) = m x + n y + p$ on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \leq 1$ by using symmetry instead of calculation

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Chapter 16.2, Problem 56E

Chapter 16.2, Problem 58E

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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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Prob. 2E Ch. 16.5 - Prob. 3E Ch. 16.5 - Prob. 4E Ch. 16.5 - Prob. 5E Ch. 16.5 - Prob. 6E Ch. 16.5 - Prob. 7E Ch. 16.5 - Prob. 8E Ch. 16.5 - Prob. 9E Ch. 16.5 - Prob. 10E Ch. 16.5 - Prob. 11E Ch. 16.5 - Prob. 12E Ch. 16.5 - Prob. 13E Ch. 16.5 - Prob. 14E Ch. 16.5 - Prob. 15E Ch. 16.5 - Prob. 16E Ch. 16.5 - Prob. 17E Ch. 16.5 - Prob. 18E Ch. 16.5 - Prob. 19E Ch. 16.5 - Prob. 20E Ch. 16.5 - Prob. 21E Ch. 16.5 - Prob. 22E Ch. 16.5 - Prob. 23E Ch. 16.5 - Prob. 24E Ch. 16.5 - Prob. 25E Ch. 16.5 - Prob. 26E Ch. 16.5 - Prob. 27E Ch. 16.5 - Prob. 28E Ch. 16.5 - Prob. 29E Ch. 16.5 - Prob. 30E Ch. 16.5 - Prob. 31E Ch. 16.5 - Prob. 32E Ch. 16.5 - Prob. 33E Ch. 16.5 - Prob. 34E Ch. 16.5 - Prob. 35E Ch. 16.5 - Prob. 36E Ch. 16.5 - Prob. 37E Ch. 16.5 - Prob. 38E Ch. 16.5 - Prob. 39E Ch. 16.5 - Prob. 40E Ch. 16.5 - Prob. 41E Ch. 16.5 - Prob. 42E Ch. 16.5 - Prob. 43E Ch. 16.5 - Prob. 44E Ch. 16.5 - Prob. 45E Ch. 16.5 - Prob. 46E Ch. 16.5 - Prob. 47E Ch. 16.5 - Prob. 48E Ch. 16.5 - Prob. 49E Ch. 16.5 - 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The average value of the linear function f ( x , y ) = m x + n y + p on the ellipse x 2 a 2 + y 2 b 2 ≤ 1 by using symmetry instead of calculation

Solution Summary: The author explains how to determine the average value of the linear function f (x, y) = m x + n p over the ellipse D by using symmetry instead of calculation.

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The average value of the linear function $f (x, y) = m x + n y + p$ on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \leq 1$ by using symmetry instead of calculation

Want to see the full answer?

Chapter 16 Solutions

The average value of the linear function f ( x , y ) = m x + n y + p on the ellipse x 2 a 2 + y 2 b 2 ≤ 1 by using symmetry instead of calculation

Solution Summary: The author explains how to determine the average value of the linear function f (x, y) = m x + n p over the ellipse D by using symmetry instead of calculation.

Videos

The average value of the linear function f(x,y)=mx+ny+p on the ellipse x2a2+y2b2≤1 by using symmetry instead of calculation

Want to see the full answer?

Chapter 16 Solutions

The average value of the linear function $f (x, y) = m x + n y + p$ on the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} \leq 1$ by using symmetry instead of calculation