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Evaluate the given definite integral.$\int_{a}^{b} k d x, k$ is a constant.

$$k(b-a)$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 6

The Definite Integral

Integrals

Missouri State University

Campbell University

Baylor 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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Determine the following:

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All right, so in this problem, I'm trying to tougher to visualize this. Um, but if you follow the process of the anti derivative, the integral of this is K X And you just think that this way as what's the derivative? That would give you just a constant. It has to be a linear function where the slope is constant, whatever that constant is. And then our notation as we go from a to B now here you have an option. You can just plug in your balance. So we're looking at K times B uh, and then K times a and then you subtract off those values. This is the correct answer, or what you could do is factor out a k um and you're left with a B minus a. Now the other piece of mount will mention it. Here is what you could have done is actually just factored out a k in front. Uh, I shouldn't say factored out in front, but this is the This is equivalent to saying K Times the integral from A to B of D. X um is actually a rule that will learn if we haven't learned already. Um, to get this correct answers, so either one of these circled in green is correct

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