2. 考研
  3. 设f(x)连续，证明：∫0x[∫0tf(u)du]dt=∫0xf(t)(x-t)dt．

设f(x)连续，证明：∫0x[∫0tf(u)du]dt=∫0xf(t)(x-t)dt．

admin2021-10-18  72
问题 设f(x)连续，证明：∫0x[∫0tf(u)du]dt=∫0xf(t)(x-t)dt．
选项
答案令F(x)=∫0xf(t)dt，则F’(x)=f(x)，于是∫0x[∫0tf(u)du]dt=∫0xF(t)dt，∫0xf(t)(x-t)dt=x∫0xf(t)dt-∫0xtf(t)dt=xF(x)-∫0xtdF(t)=xF(x)-tF(t)｜0x+∫0xF(t)dt=∫0xF(t)dt．
解析
转载请注明原文地址:https://kaotiyun.com/show/YRy4777K
0

考研数学二

相关试题推荐
随机试题
最新回复(0)