求x(2-5x)½在积分区间-1/5到1/5上的定积分,详细过程 10
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∫(-1/5->1/5) x(2-5x)^(1/2) dx
=-(2/15)∫(-1/5->1/5) x d(2-5x)^(3/2)
=-(2/15) [x.(2-5x)^(3/2) ]|(-1/5->1/5) + (2/15)∫(-1/5->1/5) (2-5x)^(3/2) dx
=-(2/15) [ 1/5 +3√3/5 ] - (4/375)[ (2-5x)^(5/2) ]|(-1/5->1/5)
=-(2/75) (1 +3√3) - (4/375)( 1 + 9√3 )
=-(14+66√3) /375
=-(2/15)∫(-1/5->1/5) x d(2-5x)^(3/2)
=-(2/15) [x.(2-5x)^(3/2) ]|(-1/5->1/5) + (2/15)∫(-1/5->1/5) (2-5x)^(3/2) dx
=-(2/15) [ 1/5 +3√3/5 ] - (4/375)[ (2-5x)^(5/2) ]|(-1/5->1/5)
=-(2/75) (1 +3√3) - (4/375)( 1 + 9√3 )
=-(14+66√3) /375
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