# Riemann Sum to an integral

• Nov 30th 2009, 10:48 AM
Velvet Love
Riemann Sum to an integral
I'm having problem with this problem. I've attached a picture, because I cannot figure out how to simplify this down to typing.

I've tried just about everything our teacher has taught/shown us, but I'm coming up with wrong answers.
• Nov 30th 2009, 11:28 AM
Remember the general form of this:

$\lim_{n->\infty}\Sigma_{k=1}^nf(a+k\Delta x)\Delta x =\int_a^bf(x)dx$

$\Delta x=\frac{b-a}{n}$

In this case, the $\Delta x=\frac{3}{n}$ since $a=0$. In the case that $f(x)=sin(x)$ we have:

The $sin(a+k\Delta x)=sin(k \Delta x)=sin\left(k\frac{3}{n}\right)$

However, you're given $sin\left(k\frac{9}{n}\right)$, so what do you have to do to $sin(x)$ to get $sin\left(k\frac{9}{n}\right)$ instead of $sin\left(k\frac{3}{n}\right)$?
• Nov 30th 2009, 11:33 AM
Velvet Love
You could multiply by 3? I just got the answer right after you replied. Thanks though. The way I did it, it didn't really stick in my head. But after reading this I feel like I've learned something. Thanks.