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  • Find the half range Fourier sine series for  in the interval (0, ).

Find the half range Fourier sine series for f(x)=x(\pi-x) in the interval (0, \pi).
                                                               

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best_answer

The formula for half range fourier series 

b_n= \frac{2}{\pi}\int_{0}^{\pi}x(\pi-x)\sin(nx)dx

    =\frac{4-2\pi n \sin(\pi n)-4\cos(\pi n)}{\pi n^3}

  To get coefficients, 

                             \frac{8}{\pi},0,\frac{8}{27\pi}, 0, \frac{8}{125\pi}

and finally

           \frac{8}{\pi}\left(\sin x+ \frac{\sin 3x}{3^3}+\frac{\sin 5x}{5^3} \right )

Posted by

avinash.dongre

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