Explanation Given: The integral, ∫ 0 π 4 tan x 2 d x . Formula used: Trapezoidal rule, ∫ a b f ( x ) d x = Δ x 2 ( f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + .... + 2 f ( x n − 1 ) + f ( x n ) ) . Simpson’s rule, ∫ a b f ( x ) d x = Δ x 3 ( f ( x 0 ) + 4 f ( x 1 ) + 2 f ( x 2 ) + .... + f ( x n ) ) . Calculation: Consider ∫ 0 π 4 tan x 2 d x for n = 4 . Now from Trapezoidal rule Δ x = b − a n = π 4 − 0 4 = π 64 Therefore, ∫ 0 π 4 tan x 2 d x = Δ x 2 ( f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + .... + 2 f ( x n − 1 ) + f ( x n ) ) = 1 2 ( π 64 ) ( f ( 0 ) + 2 f ( π 64 ) + 2 f ( 2 π 64 ) + 2 f ( 3 π 64 ) + 2 f ( 4 π 64 ) ) = 1 2 π 64 ( 2 tan ( π 64 ) + 2 tan ( π 16 ) + 2 tan ( 9 π 64 ) + 1 ) = 0

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Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 4.6, Problem 16E

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To calculate: The value of the definite integral, ∫0π4tanx2dx for n=4 by the use of the Trapezoidal rule and Simpson’s rule. Compare the results with the approximation of the integral by the use of a graphical utility.

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Chapter 4.6, Problem 15E

Chapter 4.6, Problem 17E

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Chapter 4 Solutions

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The value of the definite integral, ∫ 0 π 4 tan x 2 d x for n = 4 by the use of the Trapezoidal rule and Simpson’s rule. Compare the results with the approximation of the integral by the use of a graphical utility.

Solution Summary: The author compares the results with the approximation of the integral by the use of Trapezoidal and Simpson’s rule.

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To calculate: The value of the definite integral, ∫0π4tanx2dx for n=4 by the use of the Trapezoidal rule and Simpson’s rule. Compare the results with the approximation of the integral by the use of a graphical utility.

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Chapter 4 Solutions