(a) Explanation Given information : An ellipse is centered at the origin and has x-intercepts − 5 , 0 and 5 , 0 and y − intercepts 0 , − 2 and 0 , 2 . The portion of ellipse in the first quadrant is given by f x = 2 5 25 − x 2 for 0 ≤ x ≤ 5 . Formula used : T n = Δ x ⋅ f a 2 + f x 1 + f x 2 + ... + f x n − 1 + f b 2 Calculation : The area of the portion of ellipse in the first quadrant is given by ∫ 0 5 2 5 25 − x 2 . To find T 10 , sub-divide 0 , 5 into 10 equal subintervals of width 0.5 . So, T 10 = 5 − 0 10 ⋅ f 0 2 + f 0.5 + f 1 + f 1.5 + f 2 + f 2.5 + f 3 + f 3 (b) To determine To calculate : The approximate total area enclosed within the ellipse.

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ISBN: 9780135164884

Author: BITTINGER

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Chapter 4.7, Problem 41E

(a)

To determine

To calculate : The approximate area of the portion of ellipse that is in the first quadrant by finding T10 .

(b)

To determine

To calculate : The approximate total area enclosed within the ellipse.

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Chapter 4.7, Problem 40E

Chapter 4.7, Problem 42E

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Chapter 4 Solutions

CALCULUS+ITS APPLICATIONS

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The approximate area of the portion of ellipse that is in the first quadrant by finding T 10 .

To calculate : The approximate area of the portion of ellipse that is in the first quadrant by finding T10 .

To calculate : The approximate total area enclosed within the ellipse.

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Chapter 4 Solutions