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

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

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

03:53

Frank Lin

00:56

Amrita Bhasin

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

Missouri State University

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Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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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

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