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Evaluate the given definite integral.$\int_{0}^{1}(2 x-3) d x$

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Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 6

The Definite Integral

Integrals

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

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 integral.…

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Evaluate the definite inte…

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Okay, so we're doing the integral from zero to one of two X minus three. And what's important for you to realize in this problem is that you can do the each piece separately. So do two X DX and the minus the integral from 0 to 1 of three d X. Um, but anyway, however you do the problem, you're always going to have X add one to the exponent divided by your new expert two divided by two cancer and see electric one minus three x and then have your balance from 0 to 1. So it's nice about this. Problem is, first of all, plugging in one. For each of those you get one squared, which is still one and three times one is still three. Just make sure it's negative three and then minus plug in zero for each bound zero square to still zero and three times zero is still zero. Well, zero minus zero is still nothing. So we're just left with one minus three, which equals are correct Answer of negative two

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