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Use the properties of integrals to verify the inequality without evaluating the integrals.

$ \displaystyle 2 \le \int^1_{-1} \sqrt{1 + x^2} \,dx \le 2\sqrt{2} $

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00:54

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 2

The Definite Integral

Integration

Campbell University

Harvey Mudd College

Baylor University

University of Nottingham

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.

02:12

Use the properties of inte…

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01:54

okay. We know the squirt of one has to be less than or equal to the square root of one plus X square, which is less than or equal to the sport of two. And the reason why is because zero is between is excellent exporters between zero and one because one is less than equal to one plus X squared, which is less than or equal to two. Therefore, we know we can write this as Tuas, less than or equal to the interval from negative one to the bounds of one times good of one plus X squared de axe, which is less than equal to two time squirt of two.

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