Explanation Given information: y = 1 1 − x , [ 0 , 0.99 ] , S 100 . Formula used: Assume that f ( x ) ≥ 0 and f ′ exists and continuous on the interval [ a , b ] . The arc length over the interval is given by L = ∫ a b 1 + [ f ′ ( x ) ] 2 d x The Nth Simpson’s Rule approximately to ∫ a b f ( x ) d x is S N = 1 3 Δ x ( y 0 + 4 y 1 + 2 y 2 + ... + 2 y N − 2 + 4 y N − 1 + y N ) Where Δ x = b − a N a n d y j = f ( x j ) Calculation: Consider the given function. y = 1 1 − x y ' = 1 ( 1 − x ) 2 1 + ( y ' ) 2 = 1 + ( 1 ( 1 − x ) 2 ) 2 = 1 + 1 ( 1 − x ) 4 The arc length is given by s = ∫ a b 1 + ( y ' ) 2 d x s = ∫ 0 0.99 1 + 1 ( 1 − x ) 4 d x Using the Simpson’s Rule, we estimate he above length s as S N = 1 3 Δ x ( y 0 + 4 y 1 + 2 y 2 +

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ISBN: 9781319050740

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 8.2, Problem 18E

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The arc length of the curve y=11−x over the interval [0,0.99], using the

Simpson’s Rule SN.

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Chapter 8.2, Problem 17E

Chapter 8.2, Problem 19E

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The arc length of the curve y = 1 1 − x over the interval [ 0 , 0.99 ] , using the Simpson’s Rule S N .

Solution Summary: The author calculates the arc length of the curve using the Simpson's Rule S_N.

Concept explainers

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To find:

The arc length of the curve y=11−x over the interval [0,0.99], using the

Simpson’s Rule SN.

Want to see the full answer?

Chapter 8 Solutions

The arc length of the curve y = 1 1 − x over the interval [ 0 , 0.99 ] , using the Simpson’s Rule S N .

Solution Summary: The author calculates the arc length of the curve using the Simpson's Rule S_N.

Concept explainers

Videos

To find: The arc length of the curve y=11−x over the interval [0,0.99], using the Simpson’s Rule SN.

Want to see the full answer?

Chapter 8 Solutions

To find:

The arc length of the curve y=11−x over the interval [0,0.99], using the

Simpson’s Rule SN.