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If $ \displaystyle \int^8_2 f(x) \, dx = 7.3 $ and $ \displaystyle \int^4_2 f(x) \, dx = 5.9 $, find $ \displaystyle \int^8_4 f(x) \, dx $.
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00:32
Frank Lin
00:36
Amrita Bhasin
Calculus 1 / AB
Chapter 5
Integrals
Section 2
The Definite Integral
Integration
Campbell University
Oregon State University
Harvey Mudd College
University of Michigan - Ann Arbor
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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$$\text { If } \int_{2…
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Evaluate the integral.
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Suppose that $\int_{6}^{8}…
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Suppose that $\int_{1}^{3}…
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Suppose that $\int_{9}^{4}…
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Evaluate the definite inte…
given that we have the whole area of the integral from 2 to 8, and that is 7.3. Let's go ahead and just sketch that out here. I just drew an arbitrary graph, so this is not exactly what it looks like. Of course I'm just using this as an example. But that tells us that the area here under the curve would all be 7.3. And then we're told from 2 to 4 that the area is 5.9. So then this area here would be 5.9. The question is, what is the area than from 4 to 8. So this area here, what would that evaluate too? And to do that, we could simply subtract the total area 7.3 minus 7.3 and then minus our 5.9. And that will end up giving us just go ahead and do that out. Six. That was before and 1.4. Therefore, the missing area here must be 1.4. Because if we were to add that area 1.4 plus 5.9, that would then get us back to 7.3 as well. So that is what the missing area for the integral from 4 to 8 would have to be here.
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