Explanation Given information: ∫ 0 1 e − x d x with n = 5 where n is the number of equal subintervals Formula used: Midpoint Rule: ∫ a b f ( x ) d x ≈ [ f ( x 1 ) + f ( x 2 ) + ⋯ + f ( x n ) ] Δ x Where x 1 , x 2 , ... , x n are mid-points of the subintervals of the intervals a ≤ x ≤ b and Δ x = b − a n Calculation: For n = 5 Compare ∫ a b f ( x ) d x to ∫ 0 1 e − x d x ; it becomes a = 0 and b = 1 Therefore, Δ x = b − a n = 1 − 0 5 = 0.2 Now, a 0 = a 1 = 0 x 1 = a 0 + Δ x 2 = 0 + 0.2 2 = 0.1 x 2 = x 1 + Δ x = 0.1 + 0.2 = 0.3 x 3 = x 2 + Δ x = 0.3 + 0.2 = 0.5 x 4 = x 3 + Δ x = 0.5 + 0.2 = 0.7 x 5 = x 4 + Δ x = 0.7 + 0.2 = 0.9 By using the mid-point rule, ∫ 0 1 e − x d x = [ f ( 0

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Chapter 9.4, Problem 9E

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To calculate: The approximate value of the integral ∫01e−xdx by midpoint rule with n=5, and exact value of the integral ∫01e−xdx. Express the answer to five decimal places.

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Chapter 9.4, Problem 8E

Chapter 9.4, Problem 10E

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The approximate value of the integral ∫ 0 1 e − x d x by midpoint rule with n = 5 , and exact value of the integral ∫ 0 1 e − x d x . Express the answer to five decimal places.

Solution Summary: The author calculates the approximate and exact value of the integral for n=5 by midpoint rule.

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To calculate: The approximate value of the integral ∫01e−xdx by midpoint rule with n=5, and exact value of the integral ∫01e−xdx. Express the answer to five decimal places.

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Chapter 9 Solutions