|lnx|,x从e到1/e的积分

问题描述:

|lnx|,x从e到1/e的积分

∫[e,1/e]|lnx|dx
=∫[e,1]lnxdx+∫[1,1/e]-lnxdx
=xlnx|[e,1]-∫[e,1]dx+ [-xlnx]|[1,1/e]+∫[1,1/e]dx
=-e-(1-e)+1/e+(1/e-1)
=2/e -2

∫|lnx|dx
=[1/e,1]∫-lnxdx+[1,e]∫lnxdx
=[1/e,1][-xlnx+x] + [1,e][xlnx-x]
=1-(1/e+1/e)+0-(-1)
=2-2/e