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Find the general indefinite integral. Illustrate by graphing several members of the family on the same screen.
$ \displaystyle \int \biggl( \cos x + \frac{1}{2}x \biggr) \,dx $
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00:35
Frank Lin
00:37
Amrita Bhasin
Calculus 1 / AB
Chapter 5
Integrals
Section 4
Indefinite Integrals and the Net Change Theorem
Integration
Harvey Mudd College
University of Nottingham
Idaho State University
Boston College
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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uh we're asked to find the anti derivative of co sign effects plus one half X. Dx. And you could memorize rules because I have some students that have to memorize what they intend derivative of coastline is. But to me I just think about or what derivative, well uh something would give me co sign positive coastline and that answer is positive sign. So I have correctly done that one. And then just remember that you add one to your experiment and you multiply by the reciprocal of that exponents. So in about one half times one half, Which I know is 1/4. And I just need to remember about your plus C. So this is your correct answer and can double check that's correct by taking the derivative of them. Is it true that the derivative of Sinus Cosan? Yeah. Is it true that the derivative a warm fourth X. Squared is one fx. Yet. Is it true that the derivative of a constant zero which we don't right up here. But it is. So we have the correct answer.
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