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Integrate each of the given functions.$$\int_{0}^{\pi / 4} \frac{\tan x}{\cos ^{4} x} d x$$

$\frac{3}{4}$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 5

Other Trigonometric Forms

Integrals

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

03:09

In mathematics, precalculu…

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In mathematics, a function…

02:21

Evaluate the following int…

01:15

02:06

00:55

Find each integral.$$\…

01:39

Evaluate the integrals by …

01:07

Evaluate the integral.…

10:36

04:02

Evaluate the integral.

04:50

Use basic integration form…

03:24

you're not crazy. This problem doesn't make sense. The book has a type of I've gone ahead and corrected on the screens to go ahead and copy that down The book, for some reason, forgets the coastline acts at the back here. They literally just just don't have this part right here. They just see if this doesn't it just says later. Just sense that which doesn't make sense. You obviously need an operator for the co signer us. The function doesn't work at all. So now that headaches out of the way, let's go ahead and do some calculus. So first thing we're gonna do U substitution, we say let you equal to the co sign squared of X. Thus, we can say that D X is equal to the negative one over to co sign of acts. Sign of X, Jax. So we go ahead and be right. We rewrite this integral to say negative 1/2 of e to the power of you. Do you Now we're solving the Inderal of E to the power of you, right? We're selling this interview over here. The power of you. So let's go ahead and apply the exponential rule uh, even entire you, Izzy, the tire of you. We go ahead and plug in our salt into girls we get This is eagle to negative times E to tire of you over too. Let's go ahead and undo our use institution. We go ahead and undo our U substitution. This turns into negative, easier power of co sign squared of acts over too. The problem solved plus c are constant integration. All right. Not quite done. Were asked. Uh, we're given in general from zero to pile before. Remember, pi were for a good friend, the unit circle. Let's go ahead and evaluate this definite integral. So this turns into e for the power. Excuse me. E over to minus the square root of e over to which is equivalent to e minus the square root of e over, too. And that's our answer. Well, I'm gonna go ahead and give you a decimal proclamation, just in case of 0.3478 But go ahead and keep it in this form right here. And that's why

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