00:00Look, dx is 9x minus x square.
00:04Now, do you want to do this?
00:08This is x square.
00:11Let's take a positive and minus.
00:13x square minus 9x.
00:17Now, we will find that this is perfect square.
00:20A square minus 2ab.
00:23So, we will take a tool to ourselves.
00:259 by 2x.
00:27Now, if this is a, this is b,
00:30then 9 by 2 square plus and minus.
00:34The whole thing is not a formula.
00:39x minus 9 upon 2 square, minus 9 upon 2 square.
00:44If 9 upon 2 square is square,
00:48this will be minus minus minus plus.
00:52If this is constant square minus variable square,
00:55then x is equal to a sine theta.
00:58x's minus 9 by 2 is,
01:00and a's minus 9 by 2 is.
01:02If a square is square,
01:04then 9 by 2 is gone.
01:06Now, take a derivative.
01:08So, dx will be 9 upon 2 cos theta d theta.
01:12Now, we will not save anything.
01:13Now, then, we will notice here.
01:16So, here is the right.
01:18So, this is the right one.
01:19So, in third, we can take a more.
01:28There be 4 square minus 2.
01:29Here, we will count 9 by 2.
01:32Now, now, we will count as the right.
01:36and our square root cancels
01:39so this is 1 minus sine square which is cos square
01:43d theta in the end
01:46x minus 9 upon 2
01:48we have 9 upon 2 sine theta
01:49take the theta to one side
01:56so theta finally will be sine inverse
01:592x minus 9 upon 9 plus c
02:01this is our answer
02:04question number 12 is
02:09exercise 6.3
02:105 plus 4x minus x square
02:13this is negative time
02:15first do not positive
02:17take the minus comma
02:19and x square minus 4x
02:22this is minus 5
02:23we will make perfect square
02:24see this is minus
02:27a square minus 2a
02:30plus b square
02:59formula
03:29square minus 4x
03:303 cos theta d theta put
03:32put
03:32and x minus 2
03:35will be sine theta
04:05then we will do it
04:06if we know sine theta
04:08then theta then what will happen
04:09then theta is again
04:10what will happen
04:11then this will go
04:12sine inverse
04:12and this will be 3 divided
04:14sine inverse
04:15x minus 2 upon 3
04:17plus c
04:46and this will be the answer
04:52zero
04:57square minus x
05:16and x minus x
05:17will be the same
05:29together
05:31can
05:31grow
05:35n
05:3710 theta what will happen? 10 inverse x plus 2. The answer is theta plus c. We can write
05:4310 inverse x plus 2 plus c. So this answer will finally be question number 11.
05:53Look, question number 98 dx 16 minus x squared 5 by 2.
06:01I can write 4. I can write it. x equal to a sin theta x equal to 4 sin theta
06:08dx upon d theta 4 cos theta d theta.
06:15Now we will convert this. dx is 4 cos theta dx. 16 and x is 4 sin theta.
06:28We have put this. Now we have 4 cos theta. 4 square is 16 minus sin square.
06:3716, take a small, then 1 minus sin square cos square theta.
06:44Now we will convert this power to the power root.
06:49This power root should be cancelled.
06:50This power 5 should be cancelled.
07:02This power 5 should be cancelled.
07:06And if we gonna write 16 minus 4 square by 16 that would be cancelled.
07:13Then this works and the power root. 4 will cancel.
07:19Now we gonna write 2 square and 10 2 over 4 with 5 mean it would be無x or 2.
07:21It will cancel and 256 of the power root with aka 12 plus 2 times x equal to each 2
07:25as x equal to matter.
07:30This power loop will cancel.
07:34this's what we have to do
07:39we have to do the integration here
07:43there's 10 square square
07:45it's a direct integration of its exact negative
07:4710theta
07:48and here on the square
07:52More information, it will get a higher power.
07:58The tan square integration has 10theta and the 1 square intersection.
08:02Why did tan square upon 3 ?
08:04Now, convert 10.
08:06Like this.
08:09How does tan convert?
08:11Now, we have not done it in the sin.
08:15We have taken sin theta and we have given x into 4 sin theta.
08:19that's what we have to do with this one, so sin theta will be x upon 4,
08:21meaning perpendicular and hypertonus are available.
08:24What is the problem with base?
08:26Hypertonus square will be minus perpendicular to perpendicular square.
08:30So this will be 16 minus x square.
08:3210 theta will be perpendicular upon base,
08:35meaning 10 theta will be x upon 16 minus x square.
08:38This is what we have done with the last one.
08:40Like I have done with pencil,
08:42because we don't know what answer to this one.
08:44Now, if it's 10, then we will do it.
08:48If it's 10, then we will do it.
08:48If it's 10, then we will not add anything to it.
08:51This is 256.
08:52This is also there.
08:54Now, the cancelation,
08:57like that 3 is below,
08:58it will come up.
09:00So the cancelation,
09:01it will come up.
09:02Then we will take 256 upon.
09:05So this is our final answer.
09:10From dx,
09:11it will be x andhan.
09:12we will do 4 plus x square.
09:13It will be 3 by 2.
09:14You can see 4 minus 2 square.
09:17Look,
09:18this is the form of x equals a 10 theta.
09:22So,
09:24here we will do 2 times theta.
09:28So,
09:29if we have two-puts at the same time,
09:29dx upon d theta will be 2 seconds square theta.
09:32And dx will be 2 seconds square theta.
09:35And dx will be 2 seconds square theta d theta.
09:36be a love sub ka transfer
09:37keem
09:39tik hai
09:40johing
09:41d x ki jagha
09:43me two sige square theta
09:44luk si kata ho
09:45ye four
09:46to apeni jagha tha
09:48x ko main nike
09:49amal liya tha
09:50two ten theta
09:50tihay may kar dunga
09:52or overall
09:54bracket
09:55me power three
09:56by two
09:56tii
09:56isko na chedhen
09:57raner
09:58ab daikho
09:59yehaan two ka square
10:00four uo gaya
10:01four kawo n le
10:02one plus ten sqa
10:04eb sige sqa
10:05It should cancel the second square, but there is a problem.
10:10What is it?
10:13Look, this is the 4.
10:16What can I do?
10:19I can put a square of 2.
10:22Then the power is 3 by 2.
10:24So the square of 2 and this square will cancel.
10:27And the cube is 8.
10:28So when it's 8, this is 4, because the power is 3.
10:37The power is 2, so when we write the square of 2,
10:42it will cancel the square of 2.
10:45Then the square of 2 is 8.
10:46So here is the square of 2.
10:50So we can say that this is square of 2, and this is upon 2.
10:55hr has a square of 2.
11:232 10 theta
11:24So x upon 2 10 theta
11:27And 10 we know
11:30Perpendicular upon base
11:32Perpendicular
11:332
11:38Perpendicular x
11:39So hypotenuse
11:41Perpendicular plus base
11:42Square
11:422 square plus x square
11:49Hypotenuse
11:50Q
11:50May sine theta
11:51Complex particulates
11:53I can write found x upon Abby
11:57So this is the situation
12:02Its the root of x upon x square
12:05Alexandre
12:06Just looking at thisし
12:08Yet there is nothing to be able to do
12:10So now we convert
12:11With alpha
12:13To begin
12:14If there is a JAC
12:14So we will find an algebraic
12:17That is was correctly
12:22exercise six point three
12:24this is the whole exercise
12:27substitution on the base
12:29if you first
12:31constant square
12:33then minus variable square
12:369 minus x square
12:389 x constant
12:399 is the square
12:403 is the square
12:413 is the square
12:42then we put
12:43supposition
12:44x equal to
12:45a sine theta
12:48and if a square
12:49plus x square
12:50form
12:51plus
12:52x equal to
12:54a sine theta
12:54and if x square
12:56minus a square
12:57then x equal to
12:59a sine theta
13:01and this is the
13:02sine theta
13:03derivative
13:03cos theta
13:04ten
13:05and sec
13:08these all
13:09things
13:09we have
13:11we have
13:11we have
13:11we have
13:13okay
13:14now
13:17what do we need to tell you
13:19what do we need to tell you
13:20to tell you
13:21the first question
13:25x cube
13:27dx
13:289 minus x square
13:299 minus x square
13:32suppose
13:37position
13:37is the
13:39x
13:39we need a sine theta
13:41now
13:43if a square
13:44is 9
13:45then
13:47what do we need to tell you
13:50x equal to
13:513 sine theta
13:52now
13:52this
13:533
13:53multiply
13:54divide
13:56sine theta
13:57x upon 9
13:57now
13:58see
13:59sine theta
14:00perpendicular
14:00upon
14:01hypotenuse
14:02is the
14:02perpendicular
14:03x
14:03or hypotenuse
14:043
14:04diagram
14:053
14:07perpendicular
14:08x
14:08is the
14:09base
14:09now
14:10look
14:10I have
14:11thought
14:11when the sine
14:11is the
14:11positive
14:12involved
14:12how
14:13it is involved
14:13as we can see
14:15the base
14:16is the
14:16hypotenuse
14:17square
14:17minus
14:17perpendicular
14:18is the
14:18square
14:18minus
14:21pathogorist
14:22theorem
14:22we can see
14:24so
14:27hypotenuse
14:283
14:29is the
14:29square
14:299
14:31minus
14:32x
14:32square
14:34so
14:34this
14:36is the
14:36base
14:36is the
14:38base
14:39upon
14:39hypotenuse
14:40is the
14:41base
14:41is the
14:429
14:42minus
14:42x
14:43square
14:43hypotenuse
14:443
14:44is the
14:46main
14:469
14:47minus
14:47x
14:48square
14:48upon
14:483
14:49is the
14:52cos
14:54theta
14:54we can
14:54write
14:55here
14:55sin
14:56theta
14:56can
14:56here
14:57we can
14:58put
14:58whole
14:58converter
14:59will
14:59go
15:00x
15:01go
15:013
15:03sin
15:03theta
15:03so
15:053
15:05cube
15:0527
15:07and
15:08sin
15:08cube
15:09sin
15:09cube
15:09theta
15:10will
15:10go
15:109
15:11minus
15:12x
15:12square
15:12is the
15:16upon
15:173
15:17this is the cost theta.
15:20This means that
15:28dx upon d theta
15:31has been 3 cost theta.
15:33or dx
15:35is the cost theta
15:37d theta.
15:37This is the cost of sine theta.
15:41Now, this is the cost of sine theta.
15:43Now, what about this?
15:46So, this is the cost of sine theta.
15:48Same theta for sine theta.
15:50This has yine d theta
15:51which made the cost of sine theta.
16:08Look, we all get cut the cost of乾,
16:17So what will happen in this new step?
16:22Here is 3 square 9, 9 sine square feet.
16:269 common is 1 minus 9 square, cos square.
16:31I am doing this.
16:349 square root 3 will cut from the next step.
16:39Cos square root cause will cut from this step.
16:42Now we have 27 sine cube theta.
16:4527 will cut from this step.
16:47This sine square feet into sine theta t theta.
16:51sine square theta will be 1 minus cos square into sine theta t theta.
16:59The only integration will be 1.
17:03This will be 27 and sine theta t theta.
17:07This will be 27 and sine theta cos.
17:11Here the sign theta will be minus cos theta.
17:15The second to that is constant jetzt.
17:19We will say that the positive will over the next step as made,
17:20and we also have minus space.
17:23TheἜ hope is 0 minus 2.
17:27So here we have 2 Turtle and 1 minus cos square.
17:38There is 4eta.
17:41Then we will divide and 2 will be分ed.
17:43So this looks to theズm道 system.
17:44we will cut from 27.3
17:49so finally
17:51we will get this result
17:53minus 9 minus s square
17:56plus 9 minus s square
17:59cube upon 27
18:02this is our final answer
18:06question number 14
18:086.3 or x plus 1
18:09x square plus 2x minus 15
18:14x square plus 2x plus 1
18:16plus 1
18:17minus 1
18:18minus 15 minus 16
18:21x plus 1
18:27x square
18:28x square minus a square
18:29x square
18:30x equal to a sec theta
18:32x plus 1
18:35x plus 1
18:37x plus 1
18:37x plus 1
18:52x plus 1
18:55x plus x
19:00and the 16 root is 4
19:04and this 1 minus 1 square 10 square will be cancelled
19:07and this will cancel everything
19:08d theta upon 4 or not theta upon 4
19:11now theta to get it
19:12x plus 1 force 1 theta
19:15x plus 1 upon 4
19:16theta will be 2 inverse x plus 1 upon 4
19:21which will be 1 upon 4
19:22second inverse x plus 1 upon 4
19:24plus c
19:25this will be the answer
Comments