Thread: Please help explain definite integrals and Riemann Sums, I am so confused

My professor has not answered any of my emails regarding definite integrals. Can anyone please explain this problem and solution?

I am not sure how to put the actual formula in here but this is what I have:

Consider the function f(x)= ((x^2/2)+7)
Calculate Rn for f(x)=((x^2/2)+7) on the interval [0,3] and write your answer as a function of n without any summation signs.
Rn=______
lim Rn=______

I know that the limit is 25.5 (found on another site) but I am so confused on how to actually solve it, the answer doesn't help.

I think Xi is 3n/n and the change in X is 3/n

But I have no idea where to go from there.

Can anyone please help explain what to do?

Do you know what a Riemann sum is ? If, so just think of a definite integral as another way of compute the Riemann sum over some interval fairly easier than just adding the term of a Riemann sum to however many sub-divisions over some interval.

Here is a link that can explain better than I can:
Pauls Online Notes : Calculus I - Definition of the Definite Integral

Also for a bit help your definite integral based on the information given

Edit: Are you writing the Riemann sum of this function? or definite integral? It seems to me, I might have misread, you are trying to write this in terms of n in the form of a definite integral, then you start to mention, the change and x and such.