Math Help - riemann sum

1. riemann sum

I need to find what definite integral is approximated by $\sum_{i=1}^{50} (\frac{i}{50})^2\frac{1}{50}$ on the interval [0,1]

the answer seems to be $\int_0^1 x^2dx$ but why is it not $\int_0^1\frac{x^2}{50^3}dx$

Do I only concern myself with what is happening to i or whatever variable is used, i, k etc etc

thanks

2. Re: riemann sum

the 1/50 is the dx

3. Re: riemann sum

I kind of get it, but why not $\int_0^1 \frac{x^2}{50^2} dx$

4. Re: riemann sum

Originally Posted by Jonroberts74
I kind of get it, but why not $\int_0^1 \frac{x^2}{50^2} dx$
x[i] = i dx

x[i]2 = (i dx)2

you have a further dx from the integral itself and as dx = 1/50 you end up with

$\sum _{i=1}^{50} \left(\frac{i}{50}\right)^2 \frac{1}{50}$