设f(x)=分段函数xsinx,(x>0) -1,(x≤0),求∫(0→2π)f(x-π)dx

2025-03-01 23:05:32
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回答1:

∫(0→2π)f(x-π)dx=∫(0→π)f(x-π)dx+∫(π→2π)f(x-π)dx
=-x| 0→π +∫(π→2π)xsinxdx =-π-∫(π→2π)xdcosx=-π-[(xcosx)--∫(π→2π)cosxdx
=-π-[(xcosx)|π→2π -∫(π→2π)cosxdx]
=-π-(2π+π-0)=-4π