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Use properties of integrals, together with Exercises 27 and 28, to prove the inequality.
$ \displaystyle \int^3_1 \sqrt{x^4 + 1} \,dx \ge \frac{26}{3} $
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01:28
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 2
The Definite Integral
Integration
Missouri State University
Harvey Mudd College
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.
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okay. The comparison property of Integral says that the integral from 1 to 3 squirt of ex forth plus one, it's greater than or equal to the integral from 1 to 3 of X squared DX. Therefore, we now know the intro from 1 to 3 sort of X to the fourth plus one is greater than or equal to three cubed minus one cubed over three, which is 26 over three.
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