Problem 18. Find the Fourier approximation to f(x) = x² over the interval [-, π] using the orthogonal set of vectors U₁ = 1, u2=sin r, and U3 = COST. You may find the following integrals useful: 1 dx = 2, sin² x dx = π [co cos²x dx = π Answer: f3(x) = 2 ["2² dx = ²3², -75 [. -TT x² sin x dx = 0, [+ <-T x² cos x dx = -4T sin x + COST
Problem 18. Find the Fourier approximation to f(x) = x² over the interval [-, π] using the orthogonal set of vectors U₁ = 1, u2=sin r, and U3 = COST. You may find the following integrals useful: 1 dx = 2, sin² x dx = π [co cos²x dx = π Answer: f3(x) = 2 ["2² dx = ²3², -75 [. -TT x² sin x dx = 0, [+ <-T x² cos x dx = -4T sin x + COST
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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![Problem 18. Find the Fourier approximation to f(x) = x² over the interval [-T, T] using the orthogonal
set of vectors
U₁ = 1,
You may find the following integrals useful:
π
S
u₂ = sinx, and U3 = cos x.
1 dx 2π,
=
π
[2²
Answer: f3(x) =
x² dx
TT
[sin² zde - ² sin x dz - 0.
x dx = π
[²
dx = 0,
7
2
= 1/37³3,
[²2dx-code--4
cos² x dx = π
COS
x² cos x dx = -4π
πT
=
+
sin x +
COST](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0aa27a28-efdb-4d0f-aad3-266fe3536dfa%2Fdab1da33-1a2d-41b7-9621-3ff911d8d9c8%2Fv80b86_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 18. Find the Fourier approximation to f(x) = x² over the interval [-T, T] using the orthogonal
set of vectors
U₁ = 1,
You may find the following integrals useful:
π
S
u₂ = sinx, and U3 = cos x.
1 dx 2π,
=
π
[2²
Answer: f3(x) =
x² dx
TT
[sin² zde - ² sin x dz - 0.
x dx = π
[²
dx = 0,
7
2
= 1/37³3,
[²2dx-code--4
cos² x dx = π
COS
x² cos x dx = -4π
πT
=
+
sin x +
COST
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