Explanation Given information: ∫ 1 2 1 x + 1 d x with n = 5 where n is the number of equal subintervals Formula used: 1) 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 . 2) ∫ a b 1 a x + b = ≥ [ ln ( a x + b ) a ] | a b Calculation: For n = 5 Compare ∫ a b f ( x ) d x to ∫ 1 2 1 x + 1 d x ;it becomes a = 1 and b = 2 Therefore, Δ x = b − a n = 2 − 1 5 = 0.2 Now, a 0 = a 1 = 1 x 1 = a 0 + Δ x 2 = 1 + 0.2 2 = 1.1 x 2 = x 1 + Δ x = 1.1 + 0.2 = 1.3 x 3 = x 2 + Δ x = 1.3 + 0.2 = 1.5 x 4 = x 3 + Δ x = 1.5 + 0.2 = 1.7 x 5 = x 4 + Δ x = 1.7 + 0.2 = 1.9 By using the mid-point rule, ∫ 1 2 1 x + 1 d x = [ f ( 1

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Chapter 9.4, Problem 10E

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To calculate: The approximate value of the integral ∫121x+1dx by midpoint rule with n=5 andexact value of the integral ∫121x+1dx. Express the answer to five decimal places.

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Chapter 9.4, Problem 9E

Chapter 9.4, Problem 11E

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The approximate value of the integral ∫ 1 2 1 x + 1 d x by midpoint rule with n = 5 andexact value of the integral ∫ 1 2 1 x + 1 d x . Express the answer to five decimal places.

Solution Summary: The author calculates the approximate value of the integral by midpoint rule with n=5 and the exact value by comparing it to five decimal places.

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To calculate: The approximate value of the integral ∫121x+1dx by midpoint rule with n=5 andexact value of the integral ∫121x+1dx. Express the answer to five decimal places.

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