区间[-1.1]定积分dx/根号(5-4x)

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区间[-1.1]定积分dx/根号(5-4x)
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区间[-1.1]定积分dx/根号(5-4x)
区间[-1.1]定积分dx/根号(5-4x)

区间[-1.1]定积分dx/根号(5-4x)
F(x)=∫[1/√(5-4x)]dx
=(-1/4)∫[(5-4x)^(-1/2)]d(5-4x)
=(-1/2)(5-4x)^(1/2)+C
=(-1/2)√(5-4x)+C.
∴∫[-1,1]dx/√(5-4x)
=F(1)-F(-1)
=(-1/2)·(1-3)
=1.