Explanation Formula used: Simpson’s rule: ∫ a b f ( x ) d x ≈ h 3 ( y 0 + 4 y 1 + 2 y 2 + 4 y 3 + 2 y 4 + ⋯ + 4 y n − 1 + y n ) , where h = b − a n . Calculation: The average value of the electric current is given by the function x ¯ = 0.9129 ∫ 0 3 x 0.3 − 0.1 x d x . Divide the interval from x = 0 to x = 3 into twelve intervals. The value of h = 3 − 0 12 = 3 12 = 0.25 . Thus, the intervals are: 0 , 0.25 , 0.5 , 0.75 , 1 , 1.25 , 1.5 , 1.75 , 2 , 2.25 , 2.5 , 2.75 , 3 . Find the values of y 0 , y 1 , ⋯ and tabulate as follows. n x n y n 0 0 0 0.3 − 0.1 ( 0 ) = 0 1 0.25 0.25 0.3 − 0.1 ( 0.25 ) = 0.131 2 0.5 0.5 0.3 − 0.1 ( 0.5 ) = 0.25 3 0.75 0.75 0.3 − 0.1 ( 0.75 ) = 0.356 4 1 1 0.3 − 0.1 ( 1 ) = 0.447 5 1.25 1.25 0.3 − 0.1 ( 1.25 ) = 0.523 6 1.5 1.5 0.3 − 0.1 ( 1.5 ) = 0.581 7 1.75 1.75 0

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Chapter 25.6, Problem 17E

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The distance x¯ which is defined by x¯=0.9129∫03x0.3−0.1xdx with n = 12.

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Chapter 25.6, Problem 16E

Chapter 25.6, Problem 18E

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Chapter 25 Solutions

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

Ch. 25.1 - Find an antiderivative of x3 + 4x. Ch. 25.1 - Prob. 2PE Ch. 25.1 - Prob. 1E Ch. 25.1 - Prob. 2E Ch. 25.1 - Prob. 3E Ch. 25.1 - Prob. 4E Ch. 25.1 - In Exercises 5–12, determine the value of a that...Ch. 25.1 - Prob. 6E Ch. 25.1 - Prob. 7E Ch. 25.1 - Prob. 8E

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The distance x ¯ which is defined by x ¯ = 0.9129 ∫ 0 3 x 0.3 − 0.1 x d x with n = 12.

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The distance x¯ which is defined by x¯=0.9129∫03x0.3−0.1xdx with n = 12.

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Chapter 25 Solutions