Answered: 5. Using 4 equal-width intervals, show…

5. Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for [x²dx

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.4: Cicumference And Area Of A Cicle

Problem 18E: A rectangle has an area of 36 in2. What is the limit smallest possible value of the perimeter of the...

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5. Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for 1x²dx.

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Step 1: Given

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Step 2: Formula for trapezoidal rule, upper sum and lower sum

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Step 3: Determine the sub-intervals and function value at each value of x

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Step 4: Determine the integral using trapezoidal rule

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Step 5: Determine the integral using upper sum

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Step 6: Determine the integral using lower sum

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Step 7: Prove that the trapezoidal rule is the average of upper sum and lower sum estimation

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I have a question about the problem solved athttps://www.bartleby.com/questions-and-answers/5.-using-4-equal-width-intervals-show-that-the-trapezoidal-rule-is-the-average-of-the-upper-and-lowe/122464a7-f51e-4b62-af65-6ca354de9d6a

In step 2 shouldn't 2fx3=3, not 4.5?

Step 2
2
0
L
du
Trapezoidal vale
1h² f(x) de =
Ax =
Xo = 01
។
X 1 = xod AR = 1/₂
F(no)
f(o). O
2F(x₁) = 2f(1/₂) = 1/2 -0.5
2 F (1₂) =
2 F(^₂) =
f(14) =
A² [FR] + 2 f(x₁ + 2 f(12) -12 f(23) -1 ---+
b-a
n
i
2F(1) = 2
2F ( ¾/₂) = 4.5
f(2)=
4
2.75
2
√²x²de = 1/4 [0+0-5+2+4.5+4]
1
12 = 1 1 × 3 = ¾/1₂, xy = 2
- + f(an)]

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