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A function of period 2L has the form f(x) = L²x², xe [-L, L]. i) Compute the Fourier series for this function. ii) By choosing an appropriate value of a show that an infinite series can be con- structed for T².

A function of period 2L has the form f(x) = L²x², xe [-L, L]. i) Compute the Fourier series for this function. ii) By choosing an appropriate value of a show that an infinite series can be con- structed for T².

Advanced Engineering Mathematics
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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Question 8 A function of period 2L has the form f(x)=L²x². i) Compute the Fourier series for this function. ii) By choosing an appropriate value of a show that an infinite series can be con- structed for 7². The following indefinite integrals might be useful. L n²7² (L sin (27²) , J [₁ J ² sin ² cos x sin x Cos nTX nTX nTX ᎡᏤᏆ . L dx = dx = dx = dx = L n³73 L n³73 L n²π² x € [-L, L]. L cos 2Lnxx sin (2Lm 2LnTx cos nπx L nTX L NTX $(TTT)) + -nTX COS + nπx sin NTX L + C (2L² -n²²x²) sin +C + (2L² − n²π²x²) cos (¹T)) + ¤ (ntx)) + +C.
Transcribed Image Text:Question 8 A function of period 2L has the form f(x)=L²x². i) Compute the Fourier series for this function. ii) By choosing an appropriate value of a show that an infinite series can be con- structed for 7². The following indefinite integrals might be useful. L n²7² (L sin (27²) , J [₁ J ² sin ² cos x sin x Cos nTX nTX nTX ᎡᏤᏆ . L dx = dx = dx = dx = L n³73 L n³73 L n²π² x € [-L, L]. L cos 2Lnxx sin (2Lm 2LnTx cos nπx L nTX L NTX $(TTT)) + -nTX COS + nπx sin NTX L + C (2L² -n²²x²) sin +C + (2L² − n²π²x²) cos (¹T)) + ¤ (ntx)) + +C.
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