求定积分 ∫(上1下0)1/(x^2-2x-3)dx
问题描述:
求定积分 ∫(上1下0)1/(x^2-2x-3)dx
答
∫[0,1] 1/(x^2-2x-3)dx
=1/5∫[0,1] [1/(x-3)-1/(x+2)]dx
=1/5[ln|x-3|-ln|x+2|] [0,1]
=1/5(ln2-ln3-ln2+ln2)
=0