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Sketch the area represented by the given definite integral.$$\int_{1}^{2} \ln x d x$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 6

The Definite Integral

Integrals

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

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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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Sketch the area represente…

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Sketch the area correspond…

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Sketch the integrand of th…

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Sketch the region of integ…

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Sketch the region whose ar…

Yeah. So our task is to come up with what the graph looks like of the integral from 1 to 2 of the natural log of X dx. Now, I don't know the answer to this. This one would be difficult to find the answer of. But if we were to look at what the graph looks like, I expect my students to know what the graph of natural log is. But maybe what you just need to recognize is that X equals one. It would be your lower bound. So we started X equals one, and then your upper bound will be X equals two. So we go until we get to X equals two. Now, maybe what you what you can get away with is figuring out that natural log of one if you use a calculator is equal to zero. But I expect my students know the natural log of one is zero. And the graph of natural log looks something like this. You know, it increases like that. So from here, you can say Okay, well, if I want the area under the curve bigger than one, but smaller than two, this is the area I want. There is the area I want for this equation. And the reason why I would do that is I don't know, a natural log of two is in my head and most people don't. So this is it couldn't have answered.

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