2. 考研
  3. 设f(x)连续，x∈[0,a]且∫0af(x)dx=,求∫0adx∫xaf(x)f(y)dy.

设f(x)连续，x∈[0,a]且∫0af(x)dx=,求∫0adx∫xaf(x)f(y)dy.

admin2022-03-23  24
问题 设f(x)连续，x∈[0,a]且∫0af(x)dx=,求∫0adx∫xaf(x)f(y)dy.
选项
答案方法一： ∫0adx∫xaf(x)f(y)dy=∫0af(x)dx∫xaf(y)dy=∫0af(y)dy∫0yf(x)dx =∫0af(x)dx∫0xf(y)dy=[*][∫0af(x)dx∫xaf(y)dy+∫0af(x)dx∫0xf(y)dy] =[*]∫0af(x)dx∫0af(y)dy=[*][∫0af(x)dx]2=[*]([*])2=1 方法二： 令F(x)=∫0af(y)dy,就有F’(x)=－f(x),于是 ∫0adx∫xaf(x)f(y)dy=∫0af(x)dx∫xaf(y)dy=－∫0aF(x)d[F(x)]=[*]｜0a=1
解析
转载请注明原文地址:https://kaotiyun.com/show/XBR4777K
0

考研数学三

相关试题推荐
随机试题
最新回复(0)