Example 6 Video Example Use the Midpoint Rule with n = 5 to approximate the following integral. [²3/0x - dx Solution 6 7 8 9 The endpoints of the subintervals are 1, (See the figure below.) 5'5'5'5 and 2, so the midpoints are 1.1, 1.3, 1.5, 1.7, and Δ x = 0.2 C ● 1.2 1.4 1.8 A x 1.1 1.3 1.5 The width of the subintervals is Ax= - (2-¹) - [ so the Midpoint Rule gives the following. ²3 dx = Ax [f(1.1) + f(1.3) + f(1.5) + f(1.7) + f(1.9)] G + 13+15+17+19) (Round your answer to four decimal places.) Since f(x) = > 0 for 1 ≤ x ≤ 2, the integral represents an area, and the approximation given by the Midpoint Rule is the sum of the areas of the rectangles shown in the figure below. y 3 y = 1.6 ● 1.7 1.9
Example 6 Video Example Use the Midpoint Rule with n = 5 to approximate the following integral. [²3/0x - dx Solution 6 7 8 9 The endpoints of the subintervals are 1, (See the figure below.) 5'5'5'5 and 2, so the midpoints are 1.1, 1.3, 1.5, 1.7, and Δ x = 0.2 C ● 1.2 1.4 1.8 A x 1.1 1.3 1.5 The width of the subintervals is Ax= - (2-¹) - [ so the Midpoint Rule gives the following. ²3 dx = Ax [f(1.1) + f(1.3) + f(1.5) + f(1.7) + f(1.9)] G + 13+15+17+19) (Round your answer to four decimal places.) Since f(x) = > 0 for 1 ≤ x ≤ 2, the integral represents an area, and the approximation given by the Midpoint Rule is the sum of the areas of the rectangles shown in the figure below. y 3 y = 1.6 ● 1.7 1.9
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 76E
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