Definite integral that is equal to Riemann sums

The problem is limit as n goes to infinity, riemann sum from i=1 to n of (2/n)(1+(2i/n))^1/2

The problem I have i getting rid of the ^1/2? I was thinking that I could evaluate the sums under the square root like Riemann sum of 1 + Riemann sum of 2i/n.all under the square root. I don't think that's how I'm suppose to do it.

Any help is greatly appreciated.

The 4 integrals to choose from are

integral from 1 to 2 f(x) = (1+x)^1/2dx

integral from 1 to n f(x) = (x)^1/2dx

integral from n to 2 f(x) = (1+x)^1/2dx

integral from 1 to 3 f(x) = (x)^1/2dx

What does the does the integral from 1 to the n mean?

Re: Definite integral that is equal to Riemann sums

Quote:

Originally Posted by

**KenAdams** The problem is limit as n goes to infinity, riemann sum from i=1 to n of (2/n)(1+(2i/n))^1/2

The problem I have i getting rid of the ^1/2? I was thinking that I could evaluate the sums under the square root like Riemann sum of 1 + Riemann sum of 2i/n.all under the square root.

Any help is greatly appreciated.

The 4 integrals to choose from are

integral from 1 to 2 f(x) = (1+x)^1/2dx

integral from 1 to n f(x) = (x)^1/2dx

integral from n to 2 f(x) = (1+x)^1/2dx

integral from 1 to 3 f(x) = (x)^1/2dx

What does the does the integral from 1 to the n mean?

I do not see in the list.

But will work.

I think there is a typo in the last one.

Re: Definite integral that is equal to Riemann sums

Thank you, but how did you figure it out.? I'm stuck with removing that square root.

Re: Definite integral that is equal to Riemann sums

Quote:

Originally Posted by

**KenAdams** Thank you, but how did you figure it out.? I'm stuck with removing that square root.

Look at this. But sure to click **show steps**.

Re: Definite integral that is equal to Riemann sums

I know how to find the integrals but I don't know how to solve the Riemunns sums?

Re: Definite integral that is equal to Riemann sums