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Evaluate the given integral and check your answer.$$\int 7 e^{x} d x$$

$$7 e^{x}+c$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 1

Anti differentiation - Integration

Integrals

Missouri State University

Harvey Mudd College

Baylor 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.

01:53

Evaluate the given integra…

02:22

00:28

Find the indefinite integr…

01:07

Evaluate the integrals.

01:12

Evaluate the integral.…

02:04

03:24

01:56

all right, We're doing the integrity with integral seven e to the X DX. Um, now, don't overthink this problem, okay? Because you learn in earlier section that the derivative of E to the X is e to the X. And so if you recall that we're working backwards, um, for the inter role, eso if we have e to the X the integral of of either the X is also e to the X. I could even add a constant in here, so because we have a constant in this problem seven. But I'm going to see here if you remember the derivative of a constant times e to the X is that same constant e to the X. So to me, it makes perfect sense. Um, that if we're working backwards that this answer is just seven e to the X. But make sure you remember your plus C Why do we need a plus? C Is because if I took the derivative of this, remember, the derivative of that would equal seven e to the X and the derivative of a constant would be zero. So this constants different than this constant are here. Just so I'm clear and we don't need it right down. Plus zero. Writing down plus zero does not change the value of this eso. That's why this is your correct answer.

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