Question

高等数学题目：1/（sinθ+cosθ）在0到π/2上求定积分，怎么求最简单啊

Answer 1

sint +cost = 根号2 sin(t+pi/4)，然后用s=t+pi/4做变量替换，在对csc s进行积分即可

Answer 2

∫(0->π/2) dx/(sinx+cosx)
=(1/√2)∫(0->π/2) dx/sin(x+π/4)
=(1/√2)[ ln|csc(x+π/4) -cot(x+π/4)| ]|(0->π/2)
=(1/√2)[ ln(√2 +1) - ln(√2-1) ]