integrate-each-of-the-functions-int-04-sqrtcos-theta-sin-theta-d-theta-3

Question

Integrate each of the functions.
$$\int 0.4 \sqrt{\cos 	heta} \sin 	heta d 	heta$$

Tyler Moulton · Accepted Answer

we want to integrate the following expression. The integral of 0.4 square root costa time signed data data. To this question is testing our knowledge of methods of integration uh Saturn have a solid foundational knowledge of integral calculus to proceed. In particular. This question is testing our knowledge of what&#x27;s known as the power rule for integration. The power rule state for the integral of U. To the N. D. U. Is U. To the N plus one, divided by N plus one plus the constant of integration seat. So if we can identify U. N. N. D. U. And are integral, we can solve by the power rule. Since sign is there a co sign? We can use a rather negative sign. Is a river of coastline. We see that U. Equals cost data. Do you think this negative sign data? The data and and A. Equals one half. Thus noting the shift or rather the difference in 10.4 multiplication really without m equals one half. As well as the missing negative sign we have by the power role that are integral is negative 10.4 times two thirds coastline to three half. Let&#x27;s see or negative eight third coastline data to the five half plus C. Note that we raised. Note that this should actually be co sign data. The three half as is written in the top line above. The reason for this is that were initially have here cause I dated the one half than for our final exponentially and +13 halfs.

Foster Wisusik · Answer

Okay, This question wants us to find this anti derivative. So let&#x27;s start by making a U substitution with our angle like normal. So this means that d&#x27;you would be equal to one over to Ruth Data D theta. But we have just one over group data instead of one over to re think so. Let&#x27;s multiply both sides of this equation by two, and now we can fully substitute. So now are integral becomes the integral of co sign of you over sine squared of you times to do you or two times the integral of co sign you over Sign Square of you, do you? And now, as you can see, we can make another substitution to finish this up. So let&#x27;s pick the equal to the sign, because sign is in that squared term there. So let V equal sign you, which means that easy is equal to co sign of you, do you? And we see that does appear inner integral so we can substitute again. And this just becomes two times the integral of Devi over V squared and doing this anti derivative out, it&#x27;s just negative two divided by the close see which substituting back in. We said that V was equal to sign you, but we&#x27;re still not done because we want it back in terms of our original variable. So we said that you was equal to squared data, so this is equal to negative two over the sign squared of theta plus C, and that&#x27;s our finally

J Hardin · Answer

this problem is from Chapter seven section to problem number forty six in the book Calculus Early Transcendence. ALS eighth edition by James Door Here we have a definite integral of the square root of one minus cosign for theta. So to deal with the square root, let&#x27;s first deal with this co signing for theta. So coming over here to the right, we can apply the double angle formula and one way to state this is that co sign of two X is one minus two times science where so since we have we don&#x27;t have a two x web of fourth Ada. We should use X equals to data. So then we have co signs for data is one minus two times science where the two data, then we have one minus cosign for data is simply to sign square to data. And this means that this way room will become square root too. Times square, the science where Susanna So one must be careful here because the square root of something square isn&#x27;t necessarily the thing that&#x27;s being swear. It&#x27;s absolute value. So for that reason to be safe here, we&#x27;LL write one too Absolute value signed to theatre. So here, let&#x27;s make an observation. Due to the bounds of integration, we have that data is between zero before. So this means that tooth data is between zero in power too. So multiply each side of this inequality by two and observed that sign is positive on the interval and separate us Ziona pirates who sinus positive there and sent sinus positive. There&#x27;s no need for the absolute value sign so we could simply right I went to times scientific data, Islamics the thing that we&#x27;re integrating much easier to work with. So coming back to the original problem we have in general sealed up our floor. I grew into stone scientific data separate our work on the side Also here in this new inaugural and my help you to go ahead and do it yourself here you could take you to be to theatre, not necessary. But it might help. So here we have negative won&#x27;t too Coastline of two data. It&#x27;s over too. And we have the end points. See our own power before, so it&#x27;s gotta unplug those in. So it&#x27;s plot this constant first, So plugging in pi over four, we have co sign a power too minus cause I know. Zero. So we have got you noting from the unit circle. This is zero. That&#x27;s the one so determined. The parentheses is minus one and we have another minus one out here. So what you got? And cancel out those negatives. Take it square, too over to, and that&#x27;s our answer.

Amit Srivastava · Answer

integration of food to eat so can be heard. This edge causes what&#x27;s and and the nest trees weakened a one place cause. Cool. If it&#x27;s separate, these two parts one by food is outside. But God. So when baby food the cheetah again, this part can put an edge One place. Of course it. Thank you. Night, do you think? And this is already standard. So one by food. Do you take that? Like Baidu Data? Less Course it. Thank you to go. So take that right. Food here is teetering too. And it is signed. It picked up by e So 60 and do whatever you say, right? And goods also safe. Yeah.

Vikash Ranjan · Answer

in the problem we have in tradition. Got ta sign, Tita, did you? No cause day. But Jake, therefore minus sign. Tita, did you date was using here for minor division? Injected apart? Whole visit was when I was a kid. Born. Fine, fine. Blessed is even as minus one were five into God&#x27;s. Oh, I&#x27;m kinda sissy System answer.

Linh Vu · Answer

were you called up a weather intercourse under Uba and EU. They wish you get encoded in uber and respond even in my embassy one let&#x27;s see and in the question were given the integral on the coast I far Tita times square it under what do menace i for Tita Dita. And now it would just This one echoed you. So you cogitate humanise I for Tita, Then you ico Jude uh minus co sign Fontina on by the General when it attempts far in the front. So you had two terms farm here then Dita. And here it means that the DT time Here we go to the EU off minus far times co sign on the front it. And if I we should be able to write this integral in terms under you now. So cause I found Tita, stay the same. Square it on the new and detail because you did the year on Manus. Far cause I far, Tita. And then we say we can cancel the course I 40 time with this one. This one is a constant camping outside. Then we get echo to the minus one over far into co this Cuero we can register into the power half, do you? And now by formula, we get echo to monitor over far we and one to the power. We&#x27;re gonna treatment of two on the tree and to see, But do you echo to this one? So we&#x27;re looking, and then we get ICO Judah minus one out of six, and then we have ju minus sigh for Did, uh, about three on top, you see?

Problem

Integrate each of the functions. $$\int 8 \sin ^{…

Problem 7 Easy Difficulty

Integrate each of the functions.
$$\int 0.4 \sqrt{\cos \theta} \sin \theta d \theta$$

Answer

$-\frac{4}{15}(\cos \theta)^{3 / 2}+C$

Related Courses

Basic Technical Mathematics with Calculus

Related Topics

Discussion

Top Calculus 1 / AB Educators

Catherine R.

Heather Z.

Caleb E.

Joseph L.

Calculus 1 / AB Courses

Precalculus Review - Intro

Functions on the Real Line - Overview

Recommended Videos

Watch More Solved Questions in Chapter 28

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Caleb E.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$-\frac{4}{15}(\cos \theta)^{3 / 2}+C$

Basic Technical Mathematics with Calculus

Catherine R.

Heather Z.

Caleb E.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Catherine R.

Heather Z.

Caleb E.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus