2. 考研
  3. 设f(x)=∫0xcost/(1+sin2t)dt，求∫01f’(x)/(1+f2(x))dx．

设f(x)=∫0xcost/(1+sin2t)dt，求∫01f’(x)/(1+f2(x))dx．

admin2022-10-25  40
问题 设f(x)=∫0xcost/(1+sin2t)dt，求∫01f’(x)/(1+f2(x))dx．
选项
答案∫0π/2f’(x)/(1+f2(x))dx=∫0π/21/(1+f2(x))df(x)=arctanf(x)｜0π/2=arctanf(π/2)，因为f(π/2)=∫0π/2cost/(1+sin2t)dt=arctansint｜0π/2=π/4，所以原式=arctanπ/4．
解析
转载请注明原文地址:https://kaotiyun.com/show/CBC4777K
0

考研数学三

相关试题推荐
随机试题
最新回复(0)