设求∫02πf(x-π)dx.

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问题求∫0f(x-π)dx.

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答案0f(x-π)dx=∫0f(x-π)d(x-π)=∫πf(x)dx=∫0sinx/(1+cos2x)dx+∫0πxsin2xdx=-arctan(cosx)|0+π/2∫0πsin2xdx=-π/2+π/2×2∫∫0π/2sin2xdx=π/2+π/2×2×1/2×π/2=-π/2+π2/4.

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