2. 考研
  3. 设f(x)满足等式xf’(x)－f(x)＝，且f(1)＝4，则∫01f(x)dx＝______．

设f(x)满足等式xf’(x)－f(x)＝，且f(1)＝4，则∫01f(x)dx＝______．

admin2020-03-18  62
问题 设f(x)满足等式xf’(x)－f(x)＝，且f(1)＝4，则∫01f(x)dx＝______．
选项
答案[*]
解析 ∫01f(x)dx＝xf(x)｜01－∫01xf’(x)dx＝f(1)－∫01[f(x)＋
]dx
＝4－∫01f(x)dx＋∫01d(1－x)
＝4－∫01f(x)dx－∫01dt＝4－∫01f(x)dx－cos2θdθ
＝4－∫01f(x)dx－，
于是∫01f(x)dx＝2－．
转载请注明原文地址:https://kaotiyun.com/show/ncD4777K
0

考研数学三

相关试题推荐
随机试题
最新回复(0)