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Evaluate the given integral and check your answer.$$\int 2 e^{t} d t$$

$$2 e^{t}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 1

Anti differentiation - Integration

Integrals

Missouri State University

Oregon State University

Idaho State University

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.…

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01:45

Evaluate the integrals.

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Evaluate the following int…

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Evaluate the given definit…

01:33

OK, so don't over think this problem. I'm starting this with a a test that you don't have to do. Uh, so let me rewrite. This is D d t of e to the t. Because we learned earlier that the derivative of E to the T is e to the T. And we also learned that well, if we had a constant in here, that constant is just part of the driven, you know, stretching the function out, so to speak. So when we're tasked with finding the derivative anti derivative the integral of two e to the T GT, well, if going this way is the exact same value, well, if we do, the anti drone of them would go backwards. It's going to be the exact same value. So the answer is to e to the t, But also make sure that you do plus c Andi, this is it. You can check your work by taking the derivative of that. Well, the derivative of two e to the T plus C is to either the T plus zero, which confirms exactly what we wanted. Eso circled in green is the correct answer

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