Problem

Evaluate the integral. $ \displaystyle \int^{…

02:21

Problem 36 Easy Difficulty

Evaluate the integral.

$ \displaystyle \int^{\pi/4}_{0} \sec \theta \tan \theta \,d\theta $

Answer

$\sqrt{2}-1$

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Video Transcript

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.

Joseph R.

Topics

Integrals

Integration

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 4

Indefinite Integrals and the Net Change Theorem

Problem