[微積] 證明
1
設f:[0,1]⊆R->R為連續函數且滿足∫f(x)dx = 1/2
0
,試証存在一點p∈(0,1),使得f(p) = p
我的想法是
積分就是指函數圖形跟x軸之間的區域面積
證明若f(x)跟x=y沒有交點的話
f(x)跟x軸之間的區域面積會不等於1/2
http://ppt.cc/tufK
(圖畫的有點醜,請包涵)
我把它分兩個case
case.I.f(x)從A_1出發(紅色部分),若不能跟x=y有交點,
f(x)最後一定要停在A_2,且面積都會大於1/2(灰色部分)
case.II.f(x)從B_1出發(藍色部分),若不能跟x=y有交點,
f(x)最後一定要停在B_2,且面積都會小於1/2(灰色部分)
請問這樣算是證明嗎?
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