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Evaluate the integral.
$ \displaystyle \int^{\pi/4}_{0} \sec \theta \tan \theta \,d\theta $
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00:38
Frank Lin
00:28
Amrita Bhasin
Calculus 1 / AB
Chapter 5
Integrals
Section 4
Indefinite Integrals and the Net Change Theorem
Integration
Campbell University
Baylor University
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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How to evaluate this integ…
So here we can just refer to the table of indefinite integral given in the text book, Which states that the integral of 2nd x times tangent x. It is just equal to sequence X. So just write that down here this case seeking theater with upper ground fire for Lower bound of zero. So here you can write this out as 2nd of pi over four minus sequence of zero. So we can all right this as one over a clear sign of pirate for -1 over co sign of zero. So coastline of Pi over four is 2 over root two. Right, 1/2 over to Goes down zero. Just one to this term will be one. And We can evaluate one over to over root two to be route to over to which we can also just right as route to minus one and there's our answer.
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