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Evaluate the given integral and check your answer.$$\int x^{3} d x$$

$$x^{4} / 4+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 1

Anti differentiation - Integration

Integrals

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

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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Evaluate the given integra…

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Evaluate the integral and …

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alright, We're tasked with finding the integral where were given the integral of execute DX and what we need to do is it's basically a two step process. You look at that exponents you add one to your exponents s O. That makes it X to the fourth power three plus one is four and then I like to say divide by that new X exponents. I've heard other teachers saying multiplying by the reciprocal new exponents as I forget how to write. Well, if you divide by four, it's the same. It's multiplied by 1/4. But then you also have to write this plus c, you have to add some constant to this answer. Now, I don't know what that constant is, but this is your final answer. Now. What you also are supposed to do is find the derivative of your answer and double check that it matches this integral. Well, if you did that, you brought that four in front four. Divided by four equals one and you subtract one from that exploit, you get X cubed and the derivative of see the derivative of any constant zero. Is it true that one execute plus zero is the same as execute. Yes, it is. So we'll check Mark that. Hey, we did check our work. So circling green is the correct answer.

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