已知f“(x)在闭区间a到b上连续且f(0)=2,f(派)=1,则∫(0到派)【f(x)+f"(x)】sinxdx=?
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已知f“(x)在闭区间a到b上连续且f(0)=2,f(派)=1,则∫(0到派)【f(x)+f"(x)】sinxdx=?
高数大神~拜托了
高数大神~拜托了
![已知f“(x)在闭区间a到b上连续且f(0)=2,f(派)=1,则∫(0到派)【f(x)+f](/uploads/image/z/8797372-52-2.jpg?t=%E5%B7%B2%E7%9F%A5f%E2%80%9C%28x%29%E5%9C%A8%E9%97%AD%E5%8C%BA%E9%97%B4a%E5%88%B0b%E4%B8%8A%E8%BF%9E%E7%BB%AD%E4%B8%94f%280%29%3D2%2Cf%28%E6%B4%BE%29%3D1%2C%E5%88%99%E2%88%AB%280%E5%88%B0%E6%B4%BE%29%E3%80%90f%28x%29%2Bf%22%28x%29%E3%80%91sinxdx%3D%3F)
∫[0,π][f(x)+f"(x)]sinxdx
=∫[0,π]f(x)sinxdx+∫[0,π]f"(x)sinxdx
=∫[0,π]f(x)sinxdx+∫[0,π] sinxdf'(x)
=∫[0,π]f(x)sinxdx+sinxf'(x)[0,π] -∫[0,π] f'(x)dsinx
=∫[0,π]f(x)sinxdx-∫[0,π] f'(x)cosxdx
=∫[0,π]f(x)sinxdx-∫[0,π] cosxdf(x)
=∫[0,π]f(x)sinxdx-cosxf(x)[0,π] +∫[0,π] f(x)dcosx
=∫[0,π]f(x)sinxdx-cosxf(x)[0,π] -∫[0,π] f(x)sinxdx
=-cosxf(x)[0,π]
=f(π)+f(0)
=3
=∫[0,π]f(x)sinxdx+∫[0,π]f"(x)sinxdx
=∫[0,π]f(x)sinxdx+∫[0,π] sinxdf'(x)
=∫[0,π]f(x)sinxdx+sinxf'(x)[0,π] -∫[0,π] f'(x)dsinx
=∫[0,π]f(x)sinxdx-∫[0,π] f'(x)cosxdx
=∫[0,π]f(x)sinxdx-∫[0,π] cosxdf(x)
=∫[0,π]f(x)sinxdx-cosxf(x)[0,π] +∫[0,π] f(x)dcosx
=∫[0,π]f(x)sinxdx-cosxf(x)[0,π] -∫[0,π] f(x)sinxdx
=-cosxf(x)[0,π]
=f(π)+f(0)
=3
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