定积分习题在0到2之间e的2／x次幂的定积分.在2到e+1之间1／x-1的定积分.0到2／派之间sin的平方2／x的定积

楼上真逗,积分多了有啥用?
∫(0→2) e^(x/2) dx
= ∫(0→2) e^(x/2) d(x/2) • 2
= 2e^(x/2) |(0→2)
= 2[e^(2/2) - e^0]
= 2(e - 1)
∫(2→e + 1) 1/(x - 1) dx
= ∫(2→e + 1) 1/(x - 1) d(x - 1)
= ln(x - 1) |(2→e + 1)
= ln[(e + 1) - 1] - ln(2 - 1)
= ln(e) - ln(1)
= 1
∫(0→π/2) sin²(x/2) dx
= ∫(0→π/2) (1 - cosx)/2 dx
= (x/2 - (1/2)sinx] |(0→π/2)
= π/4 - 1/2