Mathematics, 29.01.2020 19:02 lerinmarie
The function that can satisfied area under the curve and why area is continue to positive infinity ?
Answers: 3
![[0,t]](/tpl/images/0482/9967/ae03d.png)
such that![\displaystyle[0,t]=[x_0,x_1]\cup[x_1,x_2]\cup\cdots\cup[x_{n-1},x_n]=\bigcup_{k=0}^{n-1}[x_k,x_{k+1}]](/tpl/images/0482/9967/ac434.png)
![\hat{x_k}\in[x_k,x_{k+1}]](/tpl/images/0482/9967/8577f.png)
so that the value of ![f(\hat{x_k})=\max\{[x_k,x_{k+1}]\}](/tpl/images/0482/9967/07d04.png)
. In other words, 
is specially chosen to guarantee that 
is the maximum value of 
within each corresponding subinterval.
. In the limit, these two will be exactly equal:
as 
.
diverges if 
, so the integral must also diverge.
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The function that can satisfied area under the curve and why area is continue to positive infinity ?...
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