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Use a finite sum to estimate the area under the curve using the midpoint rule f(x)=x^3 on the interval [0,2] using two rectangles and four rectangles show all work

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.3: Trigonometric Functions Of Real Numbers

Problem 65E

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Question

Use a finite sum to estimate the area under the curve using the midpoint rule

f(x)=x^3 on the interval [0,2]

using two rectangles and four rectangles

show all work

Expert Solution

Step 1

$Width of the interval [0, 2] is = 2 - 0 = 2 So for two rectangles the width of the subintervals = ∆ x = \frac{2}{2} = 1 So the partition is = 0, 1, 2 So the midpoints are 0.5 and 1.5 So the estimated area is : ∆ x [f (0.5) + f (1.5)] = 1 [0 . 5^{3} + 1 . 5^{3}] = 3.5$

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