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Raju Ram posted an Question

January 25, 2022 • 20:25 pm 30 points

X,-t

X,-T

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  Kanishk tomar

  There's no need to check even or odd in this case. Just calculate a0 value simply. Just keep one thing in mind that you separate the integrals for x and -x and check their respective limits. Just keep it simple like you solve normal fourier questions

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  Isha lohan 1

  I hope you know how to calculate Fourier series coefficients an, bn and ao. You may be able to solve this question using simple long way, but that takes time in exams, so i will tell a simple and faster way for exam. First check if the function is even or odd, for even func, cos term goes to zero, so an=0, for odd func, sin terms are zero so, bn=0. Now the above func is odd so, an=0. Bn not equal to zero. Now we have to check for ao. In fig is the formula for ao. If you clearly analyse this formula is simply the integration of the function divided by 2L. And integrating a function means, finding area under the curve, in the above given func, when you add up all negative and positive areas, it will sum upto zero, this you can visualise yourself by seeing curve, without doing any calculation. So ao becomes zero. See attached fig. But remember if the question asks you exact value of ao, and it is non zero, then you will have to solve and integrate the function with proper limits. So option D is answer

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