# Riemann integrable

• Jun 3rd 2006, 08:48 AM
Nichelle14
Riemann integrable
Let f(x) = 1/x^2 when x is between [2,3)
= 2 when x is between [3,4]

a.) prove that f(x) is Riemann integrable on [2,4]. Given epsilon is greater than 0, find a partition P... ( i have no idea what this means. :confused: )

b.) find a continuous funciton, F(x), statisfying F(x) = integral of f(t)dt from 2 to x on [2,4]
• Jun 3rd 2006, 07:02 PM
ThePerfectHacker
[QUOTE=Nichelle14]Let f(x) = 1/x^2 when x is between [2,3)
= 2 when x is between [3,4]

a.) prove that f(x) is Riemann integrable on [2,4].
Because it is countinous on this interval.
Quote:

Originally Posted by Nichelle14
Given epsilon is greater than 0, find a partition P...

I have no idea what you mean by that. Perhaps they ask to find some partion which statisfies the Riemann integral?

Quote:

b.) find a continuous funciton, F(x), statisfying F(x) = integral of f(t)dt from 2 to x on [2,4]
You have,
$\displaystyle F(x)=\int^x_2\frac{1}{t^2}dt$
Thus,
$\displaystyle \left -\frac{1}{t} \right|^x_2=-\frac{1}{x}+\frac{1}{2}$