简单计算一下即可，答案如图所示
温馨提示：答案为网友推荐，仅供参考
第1个回答 2021-08-19
第2个回答 2021-08-19
（1）I = ∫<0, 1>(x+2)de^x = [(x+2)e^x]<0, 1> - ∫<0, 1>e^xdx
= 3e-2 - [e^x]<0, 1> = 2e-1.
（2）I = ∫<0, 2>(x-2)de^x = [(x-2)e^x]<0, 2> - ∫<0, 2>e^xdx
= 2 - [e^x]<0, 2> = 3-e^2.
（3）I = (1/2)∫<1, e>lnxd(x-1)^2
= (1/2)[(x-1)^2 lnx]<1, e> - (1/2)∫<1, e>[(x-1)^2/x]dx
= (1/2)(e-1)^2 - (1/2)[x^2/2-2x+lnx]<1, e>
= (1/2)(e-1)^2 - (1/2)[e^2/2-2e+5/2] = (e^2-3)/4
= 3e-2 - [e^x]<0, 1> = 2e-1.
（2）I = ∫<0, 2>(x-2)de^x = [(x-2)e^x]<0, 2> - ∫<0, 2>e^xdx
= 2 - [e^x]<0, 2> = 3-e^2.
（3）I = (1/2)∫<1, e>lnxd(x-1)^2
= (1/2)[(x-1)^2 lnx]<1, e> - (1/2)∫<1, e>[(x-1)^2/x]dx
= (1/2)(e-1)^2 - (1/2)[x^2/2-2x+lnx]<1, e>
= (1/2)(e-1)^2 - (1/2)[e^2/2-2e+5/2] = (e^2-3)/4
相似回答