Question

求定积分∫x/(sinx)^2dx上限为3/π下限为4/π,

Answer 1

遇到三角函数考虑万能公式.∫x/(sinx)^2dx=∫x/[(1-cos2x)/2]dx=∫2x/(1-cos2x)dx=∫2x/[1-(1-tgxtgx)/(1+tgxtgx)]dx=∫2x(1+tgxtgx)/(2tgxtgx)dx=∫[x/(tgxtgx)]d(tgx) (tgx)'=(1+tgxtgx)=-x/tgx +∫(1/tgx)dx =-x/...