find-the-area-of-the-shaded-region-in-the-figure

Name: find the area of the shaded region in the figure
Uploaded: 2020-06-08
Duration: 4 min 23 s
Channel: Numerade
Description: Find the area of the shaded region in the figure.

Question

Find the area of the shaded region in the figure.

Maninder Singh · Accepted Answer

And that given figure is in this bigger. We have to find that 80 0 this shooter Did you which is green in color? And to find this area we will perceive like this way. First of all, we will find this area of sector which is red in color. I&#x27;m showing here, reading tele this video sector and subtract 80 of triangle from it. So it will give us any of that shit duty? No for finding 80 of sector. I&#x27;m going to solve it when red color So area sector is by, uh scared. He, uh 03 60. This is the formula for fine, fine area sector. The letters at us when this area No, we know that by is 22/7 the value price 22/7. The ideas here it is given to So our scare is too tends to details given one twenty&#x27;s forever, right? 1 20 over here. And work 360. No, we will solve this thing if we can. Salo 1 23 60 We get three over here. No, that is multiple eight That top numbers If we multiply 22 by two with at 44 the symbol to play 44 by two. Again, we will get 80 it and three times seven is 21. So this is 80 Kate or 21. But if you told them, you will get for rent one night or way one day. So this is our radio sector. Now let us find idiot off Grindr. So 80 off triangle is et off triangle The idea Oh, drying good. This is equal. One have are scared. Signed Tito. This is the formula for calculating area of a triangle. It just seem as one have a b scientific data. But here A and B watery disorders are concerned there. Same. We write it as one by toe are scarce scientific. Now we will put all the values over here. This is one have radius is two. We were right toe times, two dimes, sign and T days 1 20 So we were like sign 12 and d Diggory&#x27;s Now let us all this thing. We can cancel this tool with this too. This is equals to and sign 1 20 is scare Route three. What do game weekends of this stupid? This too. And we&#x27;re left with scare you city and scary property equals 1.73 1.70. No, we have to find the appreciate your region. No, I&#x27;m going to put some weight and bring with the green color. So idea off shared religion that is required area This is equals to Idi of sector, which is war when 19 minus area Brendan which is 1.73 And when you subtract them, you will get 2.46 So the area worlds to my 6 80 of the shaded region 246 scare units.

Sky Li · Answer

right. This problem. We need to find area of the shaded regions. So buy formula. We know. Ah, if we want to inter grow instead ofthe X first of the red on the integral. So the area Hey, no e coast too into grow in terms ofthe X And we know the shaded area X goes from zero to one so we can write the bound it pounds from zero to one. Okay. Ah, for here. Ah, the formula is upper curve minus the lower occur. So this will be you two The power X linus x times e to the power X square. So our next step basically is Try toe Aah! Evaluate this, integral. All right, So we can do it. Except to separately the first term. Well, the ranger grow from zero to one into the power ext the ex minus integral from zero to one times to the power X square, the ex. Okay. And the first that we know the anti directly about that. This is e to the Power X. So this is such a yeah to the power X evaluate acts because one minus X equals zero. Okay. And this term here we can bring this acts to the differential that will give us X square. So before we do that, we need two times two. So what we trick they&#x27;re using here every times two and it divided by two. So the second term will be behalf ties into grove the roads one you two the power X square King X square. And as we can see this if we use change of arable say this explorer to be another variable t Then this is you to the party. So the auntie do it Who will be itself. So this term Ah, you free right here. No B negative One half times into the power X square evaluated and ex ecos one minus x Go to zero. Right? So, in other words, this is, um So next page the first term, remember, is need to the power axe. You&#x27;re only right from one minus X equals in Cyril zero um, minus one half he to the Power X square. Valerie had taxi. Could one minus X equals zero. So no and serve. It will be the first term. Here is I e to the power of one. Linus Ito, the power zero which is what and the second term and second term is minus one half times the first of eyes that you two, the power one. So it&#x27;s just e to the tower one minus into a powered zero where she&#x27;s far and as you can see, answer will be one half times minus one, right.

Sky Li · Answer

okay for this question we see everything is represented by why, like why X equals y squared minus to an axe. Eco&#x27;s too either the power Why? So it will be more convenient for us Take the inch grow in with respect to buy So are sheeted region area A very close to the end of our world is with respect Why in the band and go goes from ninety of war here who want and ah, here by the formula is just the upper curve here Ah, there Choose sides to the power by minus the Laura curve the proble life square minus two Okay, so our next step we find ah, anti derivative of that. This will be to Apollo. Why mine is no work. Three like you. Close bye then The value of the pound boundary whyyou goes to war Kanan Lycos Nike Air War. So the result will be Mmm, minus one third plus two Miners need to empower ninety one minus Ah, my as one third times. Like you one Q, which is not a good one. Minus two. Right, So to reach out, uh, there will be cases. Plus here. Those two combined together will give us a four. And this will be too next to third. So minus. But what A To the power ninety one on minus two. Third plus whore quietness to third close four. And we can combine those two together. This&#x27;s, uh, plus ten, ten third. Okay, me minus, But over me. Close third. Right, So this will be our answer.

Sky Li · Answer

okay. As we see, this problem is represented all the function representing back why on So when they tried to evaluate the interviewer off the shaded region of Integral in terms ofthe why instead of X, um so a region a shader region, he coast too integral in terms ofthe why y in the bound for y ears go. It goes from zero to three. Here is the three here He said origin zero, they go. Well, it goes from zero to three. Ah, and angel voices just up her curved minus the lower curved upper curve. Here is this section which is to y minus y square. So why minus y square? This is the upper curve minus the lower curve is Ritchie&#x27;s. Why square minus for Why? Okay, so why square liners for what? Um and I ve Kamp Buddha by square together and the y terms together. So this will be zero to three on the double. Minus will be. Plus, So it&#x27;s six. Why? Minus to y square. You are. And the anti directive for this is, um, three y square, minus two third like you. You ready? And that had the bound Richie Savaiko two three minus like Oh two zero! Ah, and we know when while you go to zero, this whole thing is a zero. So this whole Yuko&#x27;s Tio with Plug in by three, this will be three times. Ni reaches twenty seven Linus to third times three Q b is twenty seven. So twenty seven. So the answer will be on to third times twenty seven. This is eighteen. Oh, and there will be nice.

Fuzail Shakir · Answer

Okay. So we can be right. The shaded region as so So the integral and left simplifies down to you 2/3 times X plus two to the power of three. Over to Victor. Evaluate this from zero to minus ln of the absolute value of X plus one on you to evaluate this from zero to a swell. So doing the left hand side. First we end up with 2/3 times four to the power off. Three over to which is this small? Spite by eight minus. Ln of three minus three Star final answer is 16 over three minus ln of three.

Problem

Find the area of the shaded region in the figure.

Problem 63 Hard Difficulty

Find the area of the shaded region in the figure.

Answer

$(4 \pi / 3)-\sqrt{3} \approx 2.46$

Related Courses

Precalculus Mathematics for Calculus

Related Topics

Discussion

Top Algebra Educators

Grace H.

Alayna H.

Kayleah T.

Michael J.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 6

Video Transcript

James Stewart, Lothar Redlin, Saleem Watson

Precalculus Mathematics for Calculus

Grace H.

Alayna H.

Kayleah T.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$(4 \pi / 3)-\sqrt{3} \approx 2.46$

Precalculus Mathematics for Calculus

Grace H.

Alayna H.

Kayleah T.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

James Stewart, Lothar Redlin, Saleem WatsonPrecalculus Mathematics for Calculus

Grace H.

Alayna H.

Kayleah T.

Michael J.

James Stewart, Lothar Redlin, Saleem Watson

Precalculus Mathematics for Calculus