integrate-each-of-the-functions-int_pi-3pi-2-frac2-sin-theta-d-thetasqrt1cos-theta-3

Question

Integrate each of the functions.
$$\int_{\pi / 3}^{\pi / 2} \frac{2 \sin 	heta d 	heta}{\sqrt{1+\cos 	heta}}$$

Tyler Moulton · Accepted Answer

we want to evaluate the following expression. The integral from pi over three to pi Over two have to sign data. The data divided by square root of one plus coast Data. This question is testing our knowledge of methods of integration in particular is testing our ability to You are recently learned powerful put integration which states that the integral of U. To the N. D. U. Is U. To the N plus one divided by N plus one plus. See if we identify you and Andy you in this problem we can easily use the power rule to solve so since we have one plus Costa to raise the route one half, it must be. That is are you so you as one with Costa do you? Is negative sign data the data and is equal to negative one half. So we have an extra factor of two in our integral that we carry over to the final solution so are integral. Is negative two times. To route one plus coast data. By over by over three to pi over two or other final solution four. Route 3/2 -4.

Amit Srivastava · Answer

integration. I will do Jeter toe by toe. Ah, here it is. One plus cost Frieda Digital So we can ride one plus cost to do the edge to Costco. Trita some half angle formula. We know that one plus cause to Twitter will be to cost So when Pascoe suitable half angle this back to so who will come outside the door to and ditto Roberto. This is cause pita by No, It&#x27;s a very simple to solve this question. Due to cost $3 humans signed two divided by one burger. A limit is gelato by about two. So here it is, too little too. And signed 45 by by food Men&#x27;s one by open next April. Right, Julia So too little, too upon run by

Enkhzaya Enkhtaivan · Answer

we have a kind of simple Trigon drill here, Zahra To Pike or sign Square. Same here. No, we know what one wise screw Sanskrit of data is. This&#x27;s squirt out of sign. Uh, squared off there. Now, fortunately for us over the interval, zero to pie sign is ours and non negative. So we, Khun, simply say that this is sign off there. And now this is simply called Curse on eight, Of course. Science data if Father that Syrian. Hi. Now this is native Curse. Sign off. Hi. Minus minus, which becomes a classic er, sign of serum. And that is to because percent of pious name

Robert Daugherty · Answer

Section eight to number 26 we&#x27;re looking at in a girl&#x27;s that involved powers of Signing Co sign. You should recognize that one minus co sign squared of theta is equal to the sine squared of theta, so that makes us a whole lot simpler. This is the interval from zero to pie of the square root of sine squared of theta d theta. You have to resist the urge to write that is the square root of science. Where does being signed? You have to really keep in mind that it is theat absolute value of the sign of faith a. D theta because you have to take an account that where this thing could be positive or negative so but on this case for the integral from zero to pie, I know that the sign of Fada is greater than is equal to zero when X is in that interval from zero to pie, that&#x27;s the first, the second quadrant. So that means when I&#x27;ve taken the absolute value of a positive number is just the same as taking those absolute value signs away. So this is the integral from zero to pie of the sign of fated death. Eight. If I&#x27;d gone into pied a two pie or third and fourth quadrants, I would have had to account for the negative sign. So when you integrate this, you get minus the coastline of data evaluated from zero to high. And so this becomes when you evaluate this thing a pie that&#x27;s negative, ones of the negative of negative one minus. And then when you evaluate, this is zero. Uh, you&#x27;re gonna get minus one, and so this becomes one plus one, which is two.

Amit Srivastava · Answer

here I curto Jeter, toe by toe. Signed Tito Dictator One plus cause a square Let costed a equal duty. Hence, when we portrait I call to zero, he will be one. When did I call? Toe by toe. He will be Jill. Last night is here. And if your defense it from minor scientific data later will be duty. Now we can air just a minus. Sign with changing as a limit. 0 to 1. So here it is. Duty by one plus T Square. So if 100 panel it is Dan Inverse. Steve, I won and 0 to 1. So 10. 45 then in verse one. Bye bye, Forrester.

Wen Zheng · Answer

The problem is first maker substitution on DH. Then use integration. My parts Teo Why, I&#x27;d have been to grow so faint. Signal is into girl from return of pie over to two Frito Pie. The disco fits Q times consign clear the square. The first I can use use of prostitution. But they go to data squad, then the US is the ax too. Two times you stay there. Now this integral is you called too into girl from high over two to pie. The square is facts on the deep has one half the axe and assign Get square is consign Since this integral is factual into peril from pie or two to pine one half times Max um school sign axe. Now this is Carter would have Here is one half times pi work to pie. Sykes, Jax. Now we can use integration. My pass. So the formula is into girl from a to B you be prime the axe. It&#x27;s the call to you have sleeve from a B minus in general, from a to B your prime housefly axe. Oh, our problem. We can let you is equal to x and they re prom is recalled to assign Max. Then you prom is equal to one. Read it. Sign acts now this into your office. Hans Newtown Suiza, this is X Hammes Sign. Thanks from hi over to two. Minus into your own. Your prime time squeezes. This is Sign Axe from high work. You too. Hi. I think so too. My half first term. This zero minus pi over two and interior ofthe sign Axe is negative. Kasai Axe, This&#x27;s class Sign Max from high over to too high. This is one half. I&#x27;m selective pie. Over two. They assign highs. Makes you want fine power to zero, which is the answer is half half snaked. Your power too minus one.

Problem

Rewrite the given integrals so that they fit the …

Problem 28 Easy Difficulty

Integrate each of the functions.
$$\int_{\pi / 3}^{\pi / 2} \frac{2 \sin \theta d \theta}{\sqrt{1+\cos \theta}}$$

Answer

$4 \sqrt{\frac{3}{2}}-4$

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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$4 \sqrt{\frac{3}{2}}-4$

Basic Technical Mathematics with Calculus

Anna Marie V.

Kristen K.

Michael J.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Anna Marie V.

Kristen K.

Michael J.

Joseph L.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus