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Math Help - orthogonal

  1. #1
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    orthogonal

    Show that intergrate from 0 to Pi Sinmx Sinnx dx = 0 if m doesnt = n (use trig identities)

    I know that the trig identity that I need to know is SinaSinb= 1/2[Cos(a-b)-Cos(a+b)] other then that I am lost and was wondering if someone is able to direct me the the right direction.
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  2. #2
    MHF Contributor red_dog's Avatar
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    \displaystyle\int_0^{\pi}\sin mx\sin nxdx=\frac{1}{2}\int_0^{\pi}[\cos(m-n)x-\cos(m+n)x]dx=
    \displaystyle =\left.\frac{1}{2(m-n)}\sin(m-n)x\right|_0^{\pi}-\left.\frac{1}{2(m+n)}\sin(m+n)x\right|_0^{\pi}=0
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