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Use Property 8 to estimate the value of the integral.
$ \displaystyle \int^{2\pi}_{\pi} (x - 2\sin x) \,dx $
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01:48
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 2
The Definite Integral
Integration
Oregon State University
University of Michigan - Ann Arbor
University of Nottingham
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.
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 integrals.
the first thing we can do is take the derivative, which is one minus to co sign acts we know F prime a vaccine. Other words. That derivative is equivalent to zero when Coastline X is 1/2 which happens a pile five pi over three. Therefore test the value of off of pie, which we get as high after five pi over three, which we get to be approximately 6.97 you know, pies approximately 3.14 and then lastly, off of two pi the complete circle with just 6.28 approximately 3.14 times two, which gives our expression so five pied over three plus word of three times pyre through Portland for
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