求解定积分题
∫(∏/2,0)dx/(12+13cosx)
人气:177 ℃ 时间:2020-03-23 03:43:26
解答
积分上限是π/2,积分下限是0?
∫dx/(12+13cosx),(π/2,0)
=(1/5)ln|[tan(x/2)+5]/[tan(x/2)-5]|,(π/2,0)
=(1/5)ln|[tan(π/4)+5]/[tan(π/4)-5]|-(1/5)ln|(tan0+5)/(tan0-5)|
=(1/5)ln|6/(-4)|-(1/5)|5/(-5)|
=(ln1.5)/5-(ln1)/5
=(ln1.5)/5
≈0.08109302
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