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Problem 29 Medium Difficulty

Express the integral as a limit of Riemann sums. Do not evaluate the limit.

$ \displaystyle \int^3_1 \sqrt{4 + x^2} \, dx $


$\lim _{n \rightarrow \infty} \frac{2}{n} \sum_{i=1}^{n} \sqrt{4+\left(1+\frac{2 i}{n}\right)^{2}}$


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Video Transcript

we're to rewrite the Cinta Grill. The first thing that we could calculate is what Delta Access RB is three. So we'll have B minus a three minus one or lower limit is one all over end and then that ends up giving us to over and And therefore we're going to go ahead and start off with the limit as and goes to infinity of two over and And then we have the some from I, um, hopes yeah, from I to end. And then from there we want to go ahead and pretty much copy and paste the inner part here, which is four plus accept. Our X is going to be this part here with an eye of component. And then we started from the lower limit. And so that part for the X there is going to be one plus to I over em. All of that is within the parentheses, and that's squared. And basically this will be the rewritten form of the integral from 1 to 3. There