integrate-each-of-the-given-functions-int_0pi-4-fractan-xcos-4-x-d-x-2

Question

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

Weston Bell-Geddes · Accepted Answer

you&#x27;re not crazy. This problem doesn&#x27;t make sense. The book has a type of I&#x27;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&#x27;t have this part right here. They just see if this doesn&#x27;t it just says later. Just sense that which doesn&#x27;t make sense. You obviously need an operator for the co signer us. The function doesn&#x27;t work at all. So now that headaches out of the way, let&#x27;s go ahead and do some calculus. So first thing we&#x27;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&#x27;re solving the Inderal of E to the power of you, right? We&#x27;re selling this interview over here. The power of you. So let&#x27;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&#x27;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&#x27;re given in general from zero to pile before. Remember, pi were for a good friend, the unit circle. Let&#x27;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&#x27;s our answer. Well, I&#x27;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&#x27;s why

Amrita Bhasin · Answer

Okay, given this question, we know that are you is gonna be co sign squared acts. Therefore, or 1/2 d&#x27;you is gonna be equivalent to sign axe co sign axe d X. So we know the applying the substitution. We end up with 1/2 from 1 to 1/2. And the reason why is changing elevenses integration. We have u equals 1/2 and U equals one. And then we know that we have eat the u D u. Now we know that they&#x27;re, um that the intro of either the u. D. U is either you pussy. Afterwards, the integral of eatery you is still eat of the U. S. We have 1/2 of the U from 1 to 1/2. Okay, use the fundamental theory calculus part to 1/2 of the 1/2 minus eat of the one gives us square root of e minus e fired by two, which is the same thing as 0.5347 Approximately

Amit Srivastava · Answer

figuration off Jeter Group by very food. Thick, X minus course. It&#x27;s well, this quiet late. I equal to this. Now it&#x27;s correcting Both sides go up to discredit secrets clerics unless cause graphics minus two. Sick. It&#x27;s in, too, cause it&#x27;s no easily. We can solve the questions you have to buy. Buy food. This is separate and direct Indication off this dear toe five. I food. What plus cause Do it back to and this is minus. Do you get cancer? By vital? It&#x27;s second cause will get. So finally it is Den. It&#x27;s a receiver dope. I buy food. This is you have X and cost to exercise into its buy food, and it&#x27;s easier to buy food minus two into Bye bye. So this will get value one. Here it is five. I fooled by to survive by eight if we&#x27;ll put 45 91 by food and when report zero all valuable goods minus by very so final. And there will be hi buy food minus by bay to bless by a her that we can simply say I also this is

Sid Wan · Answer

can number turn we have into world sign acto the force cause I axed the eggs His guy If we take you to be sy ox two u equals cause I X People steal over there because I have so there&#x27;s integrate We can write us you two the force thiss guys do you bridge is just While we&#x27;re far view to the books from C Can&#x27;t substitute you buy Sign that.

Vinnu M · Answer

to solve this intellectual we have toe simplify it. So let a variable you be quarto sine x So we have Do you ask? Call six DX now for the limit. We just substitute the upper and lower limits in this equation. So we have the new article in terms off you as you tickle toe sign off hero, which gives zero so long limited zero and the upper limit would be signed by by four which is worn by fruit off to. So this gives us four multiplied by you, Do you which upon solving then gives us you squared by two with a limit from zero toe one by you do. After that we have two multiplied by one by after do well squared minus zero squared you stand gives us two multiplied by one by two which uses the answer off the dedalus

Problem

Integrate each of the given functions. $$\int \fr…

Problem 17 Easy Difficulty

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

Answer

$\frac{3}{4}$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Anna Marie V.

Kayleah T.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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$\frac{3}{4}$

Basic Technical Mathematics with Calculus

Anna Marie V.

Kayleah T.

Kristen K.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Anna Marie V.

Kayleah T.

Kristen K.

Michael J.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus