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Riemann Sum Definite Integral Question

ISITIEIW

New member
Nov 4, 2013
17
So the question is Evaluate (x-2)dx as the integral goes from -2 to 2 using the definition of a definite integral, choosing your sample points to be the right endpoints of the subintervals…

Ok, so i understand how to do this problem if it gave me an actual number of interval like n=6 but it doesn't and i'm not sure how to go about actually solving it without an actual number for n.

Thanks :)
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,854
So the question is Evaluate (x-2)dx as the integral goes from -2 to 2 using the definition of a definite integral, choosing your sample points to be the right endpoints of the subintervals…

Ok, so i understand how to do this problem if it gave me an actual number of interval like n=6 but it doesn't and i'm not sure how to go about actually solving it without an actual number for n.

Thanks
Welcome to MHB, ISITIEIW! :)

I suggest you pick n equally spaced narrow rectangles numbered i = 1, ..., n.
To visualize it, you can start with n=6.
Then each rectangle will have width w=4/n.
For each rectangle we can pick an arbitrary coordinate $x_i$ between its left side and its right side. Say we pick the center, what would $x_i$ be then?
Substitute that $x_i$ in (x-2) and you get the height of each rectangle.

Can you calculate the sum of the areas of the rectangles?
And then let n go to infinity?