int(0)^(pi)sin^(3)xcos^(7)xdx=0...

`int_(0)^(pi)sin^(3)xcos^(7)xdx=0`

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If f(x) is an odd function of x, then show that, int(-a)^(a)f(x)dx=0.
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Evaluate : int(-1)^(1)|x|dx
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Show that, int(0)^(pi)xf(sinx)dx=(pi)/(2)int(0)^(pi)f(sinx)dx.
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Show : int(a)^(b)f(kx)dx=(1)/(k)int(ka)^(kb)f(x)dx
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Show : int(0)^((pi)/(2))sinxf(sin2x)dx=int(0)^((pi)/(2))cosxf(sin2x)...
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int(0)^(8pi)sin^(6)xdx=8int(0)^(pi)sin^(6)xdx
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int(-a)^(a)(xe^(x^(4)))/(1+x^(2))dx=0
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int(0)^(pi)sin^(3)xcos^(7)xdx=0
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int(-1)^(1)sin^(-1).(2x)/(1+x^(2))dx=0
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