Use multiple application of the trapezoidal rule to numerically integrate : f(x) = = 400 x ² - 900 x² +675 x ²³ - 200 x ² + 25x +0.2 from 0 to 0.8 where n-6 Exact Estimated 1 = 1.6405 I= 1.5703 with an error of 4.2813% Compare with the multiple application Trapezoidal method, where n = 2. I= 1.0688 with an error of 34.85% Formula So f(x) dx = 4x [f(x₁) + 2 f (x₁) + 2f (X₂) + ... + 2f (Xn-1) + f(xn)] Ax= b-a Xi = a +iAx
Use multiple application of the trapezoidal rule to numerically integrate : f(x) = = 400 x ² - 900 x² +675 x ²³ - 200 x ² + 25x +0.2 from 0 to 0.8 where n-6 Exact Estimated 1 = 1.6405 I= 1.5703 with an error of 4.2813% Compare with the multiple application Trapezoidal method, where n = 2. I= 1.0688 with an error of 34.85% Formula So f(x) dx = 4x [f(x₁) + 2 f (x₁) + 2f (X₂) + ... + 2f (Xn-1) + f(xn)] Ax= b-a Xi = a +iAx
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.CR: Chapter 6 Review
Problem 20CR
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Question
![Use multiple application of the trapezoidal rule to numerically
integrate
f (x)
where n=6
Exact
Estimated
1 =1.6405
I 1.5703 with an error of 4.2813%
Compare with the multiple application Trapezoidal method,
where n = 2.
I= 1.0688 with an
error of 34.85%
Formula
:
S₂° f(x) dx = 4x [f(x₁) + 2 f (x₁) + 2f (x₂) +... + 2f (Xn-1) + f(xn)]
Ax=
Xi = a +iAx
= 400 x ² - 900 x4
+675 x ²³ - 200 x² + 25x +0.2 prom 0 to 0.8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdef63d31-f865-4b68-b515-a831fa63a48e%2Ff71f9315-e104-4839-8095-9d9d072a5ec4%2Fd5w62v7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use multiple application of the trapezoidal rule to numerically
integrate
f (x)
where n=6
Exact
Estimated
1 =1.6405
I 1.5703 with an error of 4.2813%
Compare with the multiple application Trapezoidal method,
where n = 2.
I= 1.0688 with an
error of 34.85%
Formula
:
S₂° f(x) dx = 4x [f(x₁) + 2 f (x₁) + 2f (x₂) +... + 2f (Xn-1) + f(xn)]
Ax=
Xi = a +iAx
= 400 x ² - 900 x4
+675 x ²³ - 200 x² + 25x +0.2 prom 0 to 0.8
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