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Problem

Evaluate the integral. $ \displaystyle \int^3_…

02:12

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Problem 20 Easy Difficulty

Find the general indefinite integral. Illustrate by graphing several members of the family on the same screen.

$ \displaystyle \int (e^x - 2x^2) \,dx $


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00:29

Frank Lin

00:49

Amrita Bhasin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

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Integrals

Integration

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Lectures

Video Thumbnail

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

we are asked to find the integral anti directive of E. To the x minus two X. Squared. Mhm TX. And instead of memorizing rules which you could do, I just like to think of what's derivative could give me E. To the X. And that's pretty easy because it's the only function, one of the only function whose derivative is itself uh drip of E. To the X. Is E. To the X. And then the other piece. That's your power rule where you add one to your experiment and divide by your new experiment or multiply by the reciprocal of your new Excellent. Then you just need to remember your plus seed and you have the correct answer now before just moving on, I want to point out that you can check, your answer is correct by taking the derivative of each piece and double checking that that's correct. It's a dream to be. To the exceeded the ex yeah 0 to 2 thirds. Execute two X squared. Yeah. And it's a drift of of a constant which is all this is equal to zero because we don't write plus zero up here because it won't change anything. That's why we need this plus C. So we are good circled in green is correct and we can move on.

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Top Calculus 1 / AB Educators
Grace He

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Kayleah Tsai

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Lectures

Video Thumbnail

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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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