GATE CSE
First time here? Checkout the FAQ!
x
0 votes
97 views

Example of one Question for preparing exam: Fourier series of function:

be like as: $ f(x)=\frac{a_0}{2}+\Sigma_{n=1}^{\infty} (a_n \cos nx+b_n \sin nx) $

 

(Question ) so the coefficient is: $a_n=0,n=2k+1,b_n=0,n=2k$

I want to find that how the coefficient is solved, this is my approach:

$a_{n} = \frac{1}{\pi} (\int\limits_{-\pi}^{0}-1cos(nx)dx + \int\limits_{0}^{\pi}sin(x)cos(nx) dx) = \frac{1}{\pi} \int\limits_{0}^{\pi}sin(x)cos(nx) dx = \frac{1}{\pi} \frac{cos(n\pi)+1}{1-n^2}$

 

$b_{n} = \frac{1}{\pi} (\int\limits_{-\pi}^{0}-1sin(nx)dx + \int\limits_{0}^{\pi}sin(x)sin(nx) dx)=\frac{1}{\pi} (\frac{cos(nx)}{n}|_{-\pi}^{0} + \frac{\pi}{2}) = \frac{1}{\pi} (\frac{1-(-1)^n}{n}+\frac{\pi}{2}) $

 

I think my solution is wrong, anyone could help me? I so sad...

asked in Calculus by (113 points)  
edited by | 97 views
Fourier Series is out of GATE syllabus , right ?
please be kind with me, yes

Please log in or register to answer this question.



Top Users Mar 2017
  1. rude

    4018 Points

  2. sh!va

    2994 Points

  3. Rahul Jain25

    2804 Points

  4. Kapil

    2608 Points

  5. Debashish Deka

    2104 Points

  6. 2018

    1414 Points

  7. Vignesh Sekar

    1336 Points

  8. Bikram

    1218 Points

  9. Akriti sood

    1186 Points

  10. Sanjay Sharma

    1016 Points

Monthly Topper: Rs. 500 gift card

21,446 questions
26,759 answers
60,943 comments
22,955 users