estimate-the-area-of-the-region-in-the-first-quadrant-enclosed-by-ysin-2-x-and-ysin-1-x

Question

Estimate the area of the region in the first quadrant enclosed
by $y=\sin 2 x$ and $y=\sin ^{-1} x$

Gregory Higby · Accepted Answer

eso. Since they&#x27;re asking you to just an estimate, I have no problem. I&#x27;m doing this problem as a graphing calculator problem. Um, so since they only want the area in the first quadrant, um, where these two functions are, I guess the area between those two functions um, I would just do the general. You can create the enroll from going to functions. Miscellaneous. Do the general from zero to? I wonder if he&#x27;ll give me the answer for one and then just do inverse sign of X minus Sign of X X and, uh, see the answer that they give you. There&#x27;s definitely not much area in between these two functions. That&#x27;s why it&#x27;s OK. You can just get 0.111 as your approximation. Um, yeah, because you&#x27;re allowed to use a calculator. That&#x27;s all I would do. And ah just stopped at 0.111

Stephen Hobbs · Answer

the area bounded by Y equals two and like was to sign X. If from zero toe I have that is going to be this region and dark here and that is actually their intersection. Point is that pie has so we can see that from X zero taxes pie has those are going to be our limits. And then with the area between curves, we could always if one function is on top of the other one, the whole time we could do top function minus the bottom function, so to minus to sign X. And this is, of course, with respect to X, and from here we could just go ahead and take some anti derivatives. And then our final solution for this is going to end up being high minus to. But I&#x27;m kind of focusing mostly on the integration set up, since that&#x27;s often but the tricky bit with these ones here. So this is our final area between these two regions

Vinnu M · Answer

So in this question, we need to find the area off wife Equal toe finding work X. Since we know that area off a graph, it&#x27;s the integration off. Why? With respect Toe DX. So this gives us indeed, Eagle off signing worth X DX. Now, to find the limits, we already know that x zero. So this would be one off the limits. And we also know that wife equal toe bye bye. Not since why is able to buy by two. We can easily say that X would be one. So the limits would be from 0 to 1 signing worse off X dx for no. After solving this, we have integration off signing with X as X fine in worth X minus square root off one minus x squared. But the limit course from with zero one so the area would be equal toe sign in worth. Well, the one and minus so glad wrote off and it&#x27;s off minus squared. Broke off one miles the little squared. But you would give me the area as bye bye to plus one square unit. Ask the area

Robert Daugherty · Answer

it&#x27;s been problem 62 were asked to find the region bounded by the curves sign of X and the Ark Sign of X when X goes from 0 to 1/2. Easiest way to look at this as graphically. So if I look at a graph of this scenario So I&#x27;ve graft to things here I&#x27;ve graphed the sign of X So the sign of X you see in red and then the arc sine of X you see in blue And I&#x27;m looking at the interval from 0 to 1 half looking and so it looks like the arc sine of X is larger. So that&#x27;s the curve, this on top. So to find the area between the two curves, I would just need to be able to find the integral from zero toe 1/2 of the ark sign of X minus the sign of X de eggs. So that&#x27;s what I would need in order to find the answer to this particular question. Um, so let&#x27;s go do that. So, um, so in this case, my solution is going to be the interval from integral from 0 to 1/2 Thea arc sine of X minus the sign of X dx, and we&#x27;ve done this several times. This section with integration by parts. That&#x27;s how you handle this arc sine. And when you do that, you&#x27;re an end up with the enter one minus x squared the arc sine of X Excuse me, um, one minus X squared and then plus X, the arc sine of X. And then when you integrate the minus sign function, that&#x27;s where you&#x27;re going to get the co sign function and all of this evaluated from zero to 1/2. And so now we just substitute these values in. So in doing that, So if I substitute 1/2 so one minus 1/2 squared So that&#x27;s one minus 1/4 that&#x27;s 3/4. So this is the square to 3/2 is the first term, plus 1/2 the arc sine of 1/2. What angle gives you Ah sai value of 1/2 That&#x27;s pi over six plus and then the co sign of 1/2. Now substitute zero and you&#x27;re going to get the square root of one and then plus zero. And in the coastline of zero is also one. So what? We end up with here is the square root of 3/2 plus pi over 12 plus the co sign of 1/2 minus two. And then if I substitute into my calculator, this is about 20.5407 And that should match what I got on the graphs. And it s so if you look at what I have here on my grand 0.5407 I got it by substituting the actually doing the new miracle integration. And by seeing here is the value of what I just obtained a moment ago in this particular answer, so

Amrita Bhasin · Answer

okay. Using the gruff first, we show that this is our shaded region. Over here, we know this goes from 002 pi comma zero. Which means that if the area which square is 1/4 time&#x27;s 1/4 which is 1/16 that we can calculate the area to be approximately the number of squares. So 60 two ish divide by 14 times 1/4 which is 1/16 which is like 3.9. Okay, let&#x27;s calculate the exact area now. Zero pie. I noticed. These are our bounds on the graph top minus bottom. You know, the integral of sine X Executive Co Cenex. The two goes at the top. We pull out the two that&#x27;s imprint the season. Make it 1/2 on the outside, the integral of Sinus coastline. This plugging in fundamental there of calculus. This gives us four. This is really close to 3.9

Shreya Kelly · Answer

so far this problem Exes Rating from zero. The 1/2 at any party club. Fine between them, the lower limit is going to be the sine X, and the upper limit is going to be the sine inverse X. And that&#x27;s all we need to find. The area six is reading from 0 1/2 Be warned the difference between signing number six and sign ICS and integrated to find the area like want this entire shaded me Victor Integral. So signing my 60 eggs I&#x27;m spreading binding grow minus indigo&#x27;s it over one sandbanks PXE. So far, signing were six. Let&#x27;s take it on some people s u substitution. The next is going to be sci fi d X is going to be kospi dp So Simon Success p B X GDP And that&#x27;s also substitute delivers of integration and zero and 1/2 society member Ciro&#x27;s Accord API. So he is going to be in Seattle and side unless 1/2 is going to be people. So he is going to be thought ridiculous. Are pi over six That ridiculous the same as by or six. Same here, doing this in a big room. Sinek, San Diego is going to be minus plastics from seal off the 1/2. So put this. Let&#x27;s tell the integration by parts for Cosby. So let&#x27;s take P outside. Integral Cosby is sci fi Maino Stayed away. To Go Pee is one integral cost. Be a sign. Be woman bigger. So that&#x27;s B sine b minus into your love sign. B is minus farce. Be so you don&#x27;t buy our six. So that&#x27;s BioWare. Six. Empire or six is 1/2 minus minus is plus costs by our six is room three over. It&#x27;s Upstream Tzeitel. Then the peace and people would manage and we&#x27;ll be left. It costs people too serious. A lower limit. So that&#x27;s minus off course. The ka zero is one. And seeing with this one is going to be cost 1/2 minus cause Eagle so far, zero is nothing. Mark on a jumper, I kick. Okay, so the final answer is going to be by over Drug. That&#x27;s right. Three over. Two minus one, minus one. Surplus. Route 3/2 or minus two. Response. 1/2. I lose a calculator. Further cost 1/2 0.87758 So that&#x27;s takes you don&#x27;t find 88. So plus 0.88 some firewood. 12 plus for 3/2. I us three divided by dude. Yes, 7.88 When Mr is there a plan? 0078 So that sounded there. That&#x27;s my basis. It&#x27;ll plans. It does. You don&#x27;t Thank you for watching. So I liked the fine lantern. Little 0.0 Thank you.

Problem

Use a CAS to find the area enclosed by $y=3-2 x$ …

Problem 32 Easy Difficulty

Estimate the area of the region in the first quadrant enclosed
by $y=\sin 2 x$ and $y=\sin ^{-1} x$

Answer

$$
=0.16 \mathrm{sq} \text { units. }
$$

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Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals

Heather Z.

Caleb E.

Samuel H.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

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$$=0.16 \mathrm{sq} \text { units. }$$

Calculus Early Transcendentals

Heather Z.

Caleb E.

Samuel H.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

Howard Anton, Irl Bivens, Stephen DavisCalculus Early Transcendentals

Heather Z.

Caleb E.

Samuel H.

Joseph L.

$$
=0.16 \mathrm{sq} \text { units. }
$$

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals