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Evaluate the definite integral. $ \displaysty…

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Problem 67 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^2_1 x\sqrt{x - 1} \, dx $

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Frank Lin

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Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

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Integrals

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05:53

Integrals - Intro

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.

Video Thumbnail

40:35

Area Under Curves - Overview

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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Video Transcript

Okay, we know Or you is X minus one. Which means our D'YOU is one D x, which means that now we know we have to alter our limits are lower limit is gonna be simply one minus one, which is zero, and an upper limit is gonna be to minus one, cause when exes to which gives us one. You did the 1/2 is the same thing, That squirt of you. Okay, now that we've simplified, we know we can take the integral use. The power will increase the exported by 1 to 5 over to divide by the new exponents. Now use the fundamental fear of calculus we can plug in. This is equivalent to 2/5 plus 2/3 minus zero, which some pause to 16 divided by 15.

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Calculus: Early Transcendentals

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Video Thumbnail

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Video Thumbnail

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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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