# Expressing a limit as definite Integral

• Nov 22nd 2010, 02:32 PM
KelvinScc
Expressing a limit as definite Integral
Hi, I am stuck on this question that asks me to express the following limit to infinity as a definite integral.
Attachment 19808
I am sort of stuck. If let delta x=3/n and the second part equal xi, I get that it is the integral of x^9 from 0 to 8.

However shouldn't it be something else?

• Nov 22nd 2010, 02:40 PM
TheEmptySet
Quote:

Originally Posted by KelvinScc
Hi, I am stuck on this question that asks me to express the following limit to infinity as a definite integral.
Attachment 19808
I am sort of stuck. If let delta x=3/n and the second part equal xi, I get that it is the integral of x^9 from 0 to 8.

However shouldn't it be something else?

You are correct you get

$\displaystyle \displaystyle \Delta x = \frac{3}{n}$

then

$\displaystyle \displaystyle x_i=a+i\Delta x = a+\frac{3i}{n}$

When $\displaystyle i=0$ you get $\displaystyle a$ and when $\displaystyle i=n$ you get $\displaystyle b$

So from you formula $\displaystyle a=...$ and $\displaystyle b=...$

and you f is correct $\displaystyle f(x)=x^9$