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Verify that $ f(x) = \sin \sqrt[3]{x} $ is an odd function and use that fact to show that $$ 0 \le \int^3_{-2} \sin \sqrt[3]{x} \, dx \le 1 $$
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04:18
Frank Lin
Calculus 1 / AB
Chapter 5
Integrals
Section 5
The Substitution Rule
Integration
Missouri State University
Campbell University
Harvey Mudd 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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we know that we can use the metric functions as a shortcut to figure out the integral. Which means we can see if we can prove if this function is odd or even. Okay. What this means is that where we have positive acts, we're now gonna plug in negative acts, and then we're gonna simplify. As you can see, we can see we end up with negative aftereffects, Which means that half of axe is indeed an odd function. Therefore, we know there's a property that from negative, eh? Awful vax D X is equivalent to zero. Therefore, we know that without even doing any mathematical calculations, we know the solution to this is going to be zero, and this is the proof that we can drive.
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