1. Definition: The trapezoidal approximation, Tn, with n trapezoids, for the area under a curve f over interval [a, b] f(xo) + f(n) +2 f(x₁) +2[f(x)] i=1 Ax (2) dx = T₁ - 4² [1(20) + = 2 Use the given definition to show that the equation T and Rn. = AT = b-a n I₁ = a +Ax.i i = 0, 1, 2,...n Ln+ Rn holds. Hint: Remind yourself of the definitions of Ln, 2
1. Definition: The trapezoidal approximation, Tn, with n trapezoids, for the area under a curve f over interval [a, b] f(xo) + f(n) +2 f(x₁) +2[f(x)] i=1 Ax (2) dx = T₁ - 4² [1(20) + = 2 Use the given definition to show that the equation T and Rn. = AT = b-a n I₁ = a +Ax.i i = 0, 1, 2,...n Ln+ Rn holds. Hint: Remind yourself of the definitions of Ln, 2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. Definition: The trapezoidal approximation, Tn, with n trapezoids, for the area under a curve f over interval [a, b]
n-1
Ax
[
f(x) dx ≈ Tn = f(xo) + f(xn) +2Σ
i=1
Use the given definition to show that the equation Tn
and Rn.
2. Compute L4, R4 and T4 for the function f(x)=
=
2|8
=
Ax =
Ln+ Rn
2
b-a
n
3
x₁ = a + Ax.i
i = 0,1,2,...n
holds. Hint: Remind yourself of the definitions of Ln,
on interval [1,2]. Verify result from question 1. is true.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1597ed32-e45d-4583-a76f-92703bb626d9%2Fc33a88a5-9d1d-4000-a369-61a87af19593%2F1i6kkku_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Definition: The trapezoidal approximation, Tn, with n trapezoids, for the area under a curve f over interval [a, b]
n-1
Ax
[
f(x) dx ≈ Tn = f(xo) + f(xn) +2Σ
i=1
Use the given definition to show that the equation Tn
and Rn.
2. Compute L4, R4 and T4 for the function f(x)=
=
2|8
=
Ax =
Ln+ Rn
2
b-a
n
3
x₁ = a + Ax.i
i = 0,1,2,...n
holds. Hint: Remind yourself of the definitions of Ln,
on interval [1,2]. Verify result from question 1. is true.
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