帮忙求一个积分~

来源:百度知道 编辑:UC知道 时间:2024/06/01 01:51:08
∫cosα/(d+Rsinα)dα 积分变量是α 上限是2π 下限是0

∫cosα/(d+Rsinα)dα
=∫dsinα/(d+Rsinα)
=1/R*∫d(Rsinα)/(d+Rsinα)
=1/R*∫d(d+Rsinα)/(d+Rsinα)
=1/R*ln(d+Rsinα)
=1/R*[ln(d+Rsin2π)-ln(d+Rsin0)]
=1/R*(lnd-lnd)
=0

∫cosα/(d+Rsinα)dα=∫/(d+Rsinα)dsinα
=(1/R)∫1/ (d+Rsinα)d(Rsinα+d)
=(1/R)ln(d+Rsinα)|0,2π
=(1/R)lnd-(1/R)lnd
=0

原式等于∫[1/(D+Rsinα)]dsinα=(1/R)∫[1/(D+Rsinα)]d(D+Rsinα)=(1/R)ln(D+Rsinα) 然后把上下限代进去,结果为零。