2. 考研
  3. 设f(x)在[a，b]上连续，证明：∫abf(x)dx∫abf(y)dy=[∫abf(x)dx]2．

设f(x)在[a，b]上连续，证明：∫abf(x)dx∫abf(y)dy=[∫abf(x)dx]2．

admin2016-10-13  19
问题 设f(x)在[a，b]上连续，证明：∫abf(x)dx∫abf(y)dy=[∫abf(x)dx]2．
选项
答案令F(x)=∫axf(t)dt， 则∫abf(x)dx∫xbf(y)dy=∫abf(x)[F(b)一F(x)]dx =F(b)∫abf(x)dx—∫abf(x)F(x)dx=F2(b)一∫abF(x)dF(x) =F2(b)一[*][∫abf(x)dx]2．
解析
转载请注明原文地址:https://jikaoti.com/ti/drwRFFFM
0

考研数学一

相关试题推荐
随机试题
最新回复(0)