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: The area bounded by y = sin x , y = 0 and x = π 6 is given by the integral, ∫ 0 π 6 sin x d x . First obtain the value of the integral ∫ 0 π 6 sin x d x by direct integration as shown below. ∫ 0 π 6 sin x d x = [ − cos x ] 0 π 6 = − cos ( π 6 ) − ( − cos 0 ) = − ( 3 2 ) + 1 = − 3 + 2 2 On further simplification, ∫ 0 π 6 sin x d x = 0.267949192 2 = 0.133974596 ≈ 0.134 Now substitute the first two terms of the series expansion for sin x and obtain the integral value of ∫ 0 π 6 sin x d x as shown below

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Chapter 30.3, Problem 34E

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The area bounded by y=sinx, y=0 and x=π6 by using series expansion for sinx and compare with the direct integral value.

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Chapter 30.3, Problem 33E

Chapter 30.3, Problem 35E

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Chapter 30 Solutions

Basic Technical Mathematics

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 area bounded by y = sin x , y = 0 and x = π 6 by using series expansion for sin x and compare with the direct integral value.

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