Explanation Given: The integral is ∫ 2 10 x x − 1 d x and n = 4 Approach: Simpson’s rule- Let f be a continuous function on interval [ a , b ] . We subdivide the interval into n number of pieces. Length of each subinterval is Δ x = b − a n End points of each subinterval is x 0 = a x 1 = a + Δ x x 2 = a + 2 Δ x x 3 = a + 3 Δ x . . . x n = a + n Δ x Hence approximation of integral according to Simpson’s rule is ∫ a b f ( x ) d x = Δ x 3 [ f ( x 0 ) + 4 f ( x 1 ) + 2 f ( x 2 ) + 4 f ( x 3 ) + 2 f ( x 4 ) + ........... + 4 f ( x n − 1 ) + f ( x n ) ] Calculation: Given integral is ∫ 2 10 x x − 1 d x We have a = 2 , b = 10 Therefore length of each subinterval is Δ x = 10 − 2 4 = 8 4 = 2 End point of each subinterval is x 0 = 2 x 1 = 2 + 2 = 4 x 2 = 2 + 2 × 2 = 6 x 3 = 2 + 3 × 2 = 8 x 4 = 2 + 4 × 2 = 10 We have to find value of function at each end point of interval. Hence value of function at x = 2 f ( 2 ) = 2 2 − 1 = 2 Value of function at x = 4 f ( 4 ) = 4 4 − 1 = 4 3 = 1.3333 Value of function at x = 6 f ( 6 ) = 6 6 − 1 = 6 5 = 1

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Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

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Chapter 8.CR, Problem 20CR

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Approximate the integral ∫210xx−1dx using Simpson’s rule with n=4 and also compare it with exact value of integral.

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Chapter 8.CR, Problem 19CR

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Approximate the integral ∫ 2 10 x x − 1 d x using Simpson’s rule with n = 4 and also compare it with exact value of integral.

Solution Summary: The author explains how to approximate the integral using Simpson's rule with n=4 and compare it with exact value of integral.

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To find:

Approximate the integral ∫210xx−1dx using Simpson’s rule with n=4 and also compare it with exact value of integral.

Want to see the full answer?

Chapter 8 Solutions

Approximate the integral ∫ 2 10 x x − 1 d x using Simpson’s rule with n = 4 and also compare it with exact value of integral.

Solution Summary: The author explains how to approximate the integral using Simpson's rule with n=4 and compare it with exact value of integral.

Concept explainers

Videos

To find: Approximate the integral ∫210xx−1dx using Simpson’s rule with n=4 and also compare it with exact value of integral.

Want to see the full answer?

Chapter 8 Solutions

To find:

Approximate the integral ∫210xx−1dx using Simpson’s rule with n=4 and also compare it with exact value of integral.