Explanation Formula used: Maclaurin expansion of sin x : “The Maclaurin expansion of sin x is given by, sin x = x − x 3 3 ! + x 5 5 ! − x 7 7 ! + ⋯ ” Calculation: First obtain the Maclaurin expansion of sin x 2 as follows. Replace x by x 2 in the Maclaurin expansion of sin x and obtain the Maclaurin expansion of sin x 2 as follows. sin x 2 = x 2 − ( x 2 ) 3 3 ! + ( x 2 ) 5 5 ! − ( x 2 ) 7 7 ! + ⋯ = x 2 − x 6 6 + x 10 120 − x 14 5040 + ⋯ Now obtain the value of the integral ∫ 0 1 sin x 2 d x as shown below

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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Author: Allyn Washington, Richard Evans

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Chapter 30.3, Problem 11E

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To evaluate: The integral ∫01sinx2dx using the first three terms of the series of sinx2.

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Chapter 30.3, Problem 10E

Chapter 30.3, Problem 12E

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Chapter 30 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 30.1 - Prob. 1PE Ch. 30.1 - Prob. 2PE Ch. 30.1 - Prob. 1E Ch. 30.1 - Prob. 2E Ch. 30.1 - Prob. 3E Ch. 30.1 - Prob. 4E Ch. 30.1 - Prob. 5E Ch. 30.1 - Prob. 6E Ch. 30.1 - Prob. 7E Ch. 30.1 - Prob. 8E

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The integral ∫ 0 1 sin x 2 d x using the first three terms of the series of sin x 2 .

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To evaluate: The integral ∫01sinx2dx using the first three terms of the series of sinx2.

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Chapter 30 Solutions