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Use a graph to give a rough estimate of the area of the region that lies under the given curve. Then find the exact area.
$ y = 2 \sin x - \sin 2x $, $ 0 \le x \le \pi $
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Calculus 1 / AB
The Substitution Rule
Missouri State University
Oregon State University
University of Nottingham
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.
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.
Use a graph to give a roug…
Use a graphing utility, wh…
Find the area of the regio…
okay. Using the gruff first, we show that this is our shaded region. Over here, we know this goes from 002 pi comma zero. Which means that if the area which square is 1/4 time's 1/4 which is 1/16 that we can calculate the area to be approximately the number of squares. So 60 two ish divide by 14 times 1/4 which is 1/16 which is like 3.9. Okay, let's calculate the exact area now. Zero pie. I noticed. These are our bounds on the graph top minus bottom. You know, the integral of sine X Executive Co Cenex. The two goes at the top. We pull out the two that's imprint the season. Make it 1/2 on the outside, the integral of Sinus coastline. This plugging in fundamental there of calculus. This gives us four. This is really close to 3.9
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