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Dz { 1 Jc integral following of the answer What is theIW "P 0 b. 27 8 8 6...

Question

Dz { 1 Jc integral following of the answer What is theIW "P 0 b. 27 8 8 6

dz { 1 Jc integral following of the answer What is the IW "P 0 b. 27 8 8 6



Answers

If $I_{n}=\int_{0}^{\pi / 2} x^{n} \sin x d x, n>1$, then the value of $I_{8}+56 I_{6}$ is (a) $\frac{\pi^{7}}{16}$ (b) $\frac{\pi^{6}}{32}$ (c) $\frac{\pi^{5}}{8}$ (d) $\pi^{8}$

So we want to find the following definition A rule. So remember we know that if we have an integral from A to B, um and Ar Inte Grant is a constant functions, say h D X. So this this integration does not depend on X at all. We can write this as a church times, the upper limit minus the lower limit. So b minus A. So we can use that fact here, since eight does not depend on our at all. So this is going to be equal to eight times b minus A. So negative one minus negative want, But negative 1 -2 is equal to zero. So um this integral is going to be equal to zero as well.

Oh yeah, whether given integer the substitute, he would for two x plus b so differentiating both sides will have. Do you goto 80 x So one by a do you tickle toe the X So using the substitution and Tillerson becomes one by and Tillerson do you buy you, which is all to one by day. Ellen, you Let's see which is a full 21 by a then X plus B. Let's see, there's no final answer.

Very obviously the person apart from a functionary and from here together is the person apart from maybe had given up Thanks Mr do. Oh and this guy's got a good deal. Uh In this case it's going to be like nearly one. So you can see that difference is one minute is priority here. We have action part function is priority here. You can see the building giving huh? It is periodic with period one the biggest recording with period one night to see here. Although the form has given us uh the door to zero plus six times a period. That is one time work. The function is periodic now and we'll depression part of it. Whole body person. Barbara back. Yeah now it is periodic. So this has given us we already have done in what we do and therefore that it has given us six times we have There are 2 1 and then now there are 21 there the one being attraction part of ex uh given a negative little only for dinner to one. This is 01 or 0 to 1. Was given a section about the ex uh negative. We have written it up on the next 40 to 10211. And not included. That is coming out to be a negative report away. We'll leave it at that time and work. Mhm. All here and then the you go up here so that's coming up people do six times your blind your highlight integration by parts. So this is the first function and one will be the second function so we get right in world. Thanks both. Field time in divisional wanted it X. Negative we have uh that you're doing fine work that close to it overthrew one negative expiry time. Yes and it was from they're the one This is wrong to Wall Street and the bankers we get six times that's coming out to be signed gloves. Uh one that is by over to surprise our fall 10 1 negative you will get legal and then you have negative although this coming up to be here while solving this so that's all set ready this body will have sold separately sort of doing as a two interational rehabs are yes time was that or world road one negative direct were and this coming out to be yeah and it's so it is work on it you can just I think Alex temper by any vertex so you don't for client data for doing you will get two times uh coming up to be actors time leader playing worked expose you got them vehicles 40,000 hidden for visitors coming up with the expo where crocodiles one -X. Pill will be gone. Did you the limits you have from there to one it was there for one year But then becoming working that we have designed with literally zero to buy over to the limits day it's even more beyond this so like any ammunition by a part of this is uh and that you can take this into the bus function as they can function the arena. So two times you have then data times integration of this negative partita From there to buy over two and then you have Negative The New Year 2001. The negative growth data. Did they die from the rubble by over with all the sand in get here you will die in this coming out to be negative. You have from Bolivia there are two by over fuel that's coming up to be followed by over two is zero then it's not the leader here and all that. And it will be Client data from 0 to Pi over two. It will be two times and power to is one 21 ends. Uh To hear you have you will get you so now the next it doesn't even ask. So next to this work home so we have got here uh so that they come here coming activate through here. Those will become uh three by square. Or we have to negative drill coming out to be three five field negative eight. Or would you So three bites the negative age or were true. No wonder then it is coming up to the option C. Big orbit steve thank you

In the execution we have to solve the integration that is from zero to infinity dx upon one plus X to the power nine into one plus access square. Now I'm going to assume X is equal to 10 to to. So I can say that the X is equal to six square teeter into data. Now the limit is when X is equal to zero, he doesn't is also zero and when X equals to infinity we can say that Toyota is by by two. So finally we can see that our integration is 0 to pi by two and this is shaky square twitter digital upon one plus 10 to the power 90 to into this is one plus Danny square data. So when you said that these two will cancel out and finally We get this is 0 to Pi by two. Date it up on one plus 10 to the power 90 to this is nine. Now I am going to simplify this So we will get this is you know to pay by two because 20 lb 90 to upon signed to the 1990 to plus cost to the power 90 to data. Now I'm going to apply here property that is integration zero to a F X D X can be written as zero to a F of a minus X. The this is the property and I'm going to apply this year that this is a situation first so I equals two. This is zero to Pi by two. This will comes out to be signed 90 to data upon. This is cause 90 to assigned to the power 90. To now I'm going to apply now I'm going to add both this equation and I will get that why is equals to this is bye bye to. So from here I get Isaac was two by by four so this is the answer of our given to shin here I'm adding one end equation too So this is our answer and four dead option C. Is the correct option. Thank you


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