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The Fourier series expansion of x3 in the interval −1 ≤ x < 1 with periodic continuation has
  • a)
    only sine terms
  • b)
    only cosine terms
  • c)
    both sine and cosine terms
  • d)
    only sine terms and a non-zero constant
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The Fourier series expansion of x3 in the interval −1 ≤ x <...
f(x) = x3
find f(x) is even or odd
put x = -x
f(-x) = - x3
f(x) = -f(-x) hence it is odd function
for odd function, ao = an = 0 
Fourier Series for odd function has only bn term

Hence only sine terms are left in Fourier expansion of x3
Additional Information
Fourier Series
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The Fourier series expansion of x3 in the interval −1 ≤ x < 1 with periodic continuation hasa)only sine termsb)only cosine termsc)both sine and cosine termsd)only sine terms and a non-zero constantCorrect answer is option 'A'. Can you explain this answer?
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