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How To Calculate Quickly And Correctly In Mathematics - Education (5) - Nairaland

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Re: How To Calculate Quickly And Correctly In Mathematics by lavosier: 1:45pm On Sep 16, 2013
Mbahchiboy: WORKINGS PLZ
$(cosecx) multiply nd divide tru by(cosecX + CotX)=
$cosecX((cosecX+cotX)/cscX + cotX)dx..let u =cscx + cotX..du=(-ccosecXcotX-cscX)dx..substitute du=-$(csc^2X-cscXcotX)dx/cscX + cotX=-$du/u=-inU +C den u substitute bak...
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 6:37pm On Sep 16, 2013
lavosier:
$(cosecx) multiply nd divide tru by(cosecX + CotX)=
$cosecX((cosecX+cotX)/cscX + cotX)dx..let u =cscx + cotX..du=(-ccosecXcotX-cscX)dx..substitute du=-$(csc^2X-cscXcotX)dx/cscX + cotX=-$du/u=-inU +C den u substitute bak...

Spot on bruv. Ehen, you said that the no 2 of your questions you posted at the gurus' thread has been solved. Would you mind sharing the solution with me pls?
Re: How To Calculate Quickly And Correctly In Mathematics by MrCalculus(m): 6:55pm On Sep 16, 2013
Ortarico:

Spot on bruv. Ehen, you said that the no 2 of your questions you posted at the gurus' thread has been solved. Would you mind sharing the solution with me pls?
I SIGHT U CHIEF
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 7:11pm On Sep 16, 2013
Kudos to everybody here
Re: How To Calculate Quickly And Correctly In Mathematics by MrCalculus(m): 7:18pm On Sep 16, 2013
Calculusf(x):
Kudos to everybody here
I SIGHT U @D G.THREAD BRO.
KUDOZ!!
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 11:04pm On Sep 16, 2013
Mr Calculus: I SIGHT U CHIEF

Thanks boss, 1 luv! @calculusf(x), greetings prof. You're doing a good job. I can see the both of you at the top!
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 7:23am On Sep 17, 2013
Morning to all my generals...
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 8:25am On Sep 17, 2013
....Integrate xarcsinx.dx....
Re: How To Calculate Quickly And Correctly In Mathematics by SirChides(m): 10:32am On Sep 17, 2013
Calculusf(x):
....Integrate xarcsinx.dx....
i think datz x/root(1-x^2) -root(1-x^2)+c
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 10:53am On Sep 17, 2013
Sir Chides: i think datz x/root(1-x^2) -root(1-x^2)+c
...hmmm,no sir...try more sir...let me give you hint...use integration by parts...let u be arcsinx and v be x...
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 11:12am On Sep 17, 2013
Ortarico:

Spot on bruv. Ehen, you said that the no 2 of your questions you posted at the gurus' thread has been solved. Would you mind sharing the solution with me pls?
...i'm not that very good at hyperbola...but using the equation in canonical form...(x-x')²/a²-(y-y')²/b²=1...remember that the asymptotes of an hyperbola is ±b/a and the asymptotes of the question is ±3...it means b=3 and a=1...which passes through the points 4,6...substitute that to the question to get...(x-4)²/1²-(y-6)²/3²=1...(x-4)²-(y-6)²/9=1...then complete it sir...
Re: How To Calculate Quickly And Correctly In Mathematics by lavosier: 11:31am On Sep 17, 2013
Calculusf(x):
...hmmm,no sir...try more sir...let me give you hint...use integration by parts...let u be arcsinx and v be x...
(1/2)x^2arcsinx-(1/4)arcsinx+1/4xsqreroot of (1-x^2)+c..ope am crrect??
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 11:46am On Sep 17, 2013
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Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 11:46am On Sep 17, 2013
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Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 11:50am On Sep 17, 2013
^ thanks to my star. Alas, got posted!
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 11:58am On Sep 17, 2013
Calculusf(x):
...i'm not that very good at hyperbola...but using the equation in canonical form...(x-x')²/a²-(y-y')²/b²=1...remember that the asymptotes of an hyperbola is ±b/a and the asymptotes of the question is ±3...it means b=3 and a=1...which passes through the points 4,6...substitute that to the question to get...(x-4)²/1²-(y-6)²/3²=1...(x-4)²-(y-6)²/9=1...then complete it sir...

Thanks boss it helped.
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 12:49pm On Sep 17, 2013
Ortarico:


Hmmmmmm. . . .

§ xarcsinx
integrating by parts:
let u = x; dv = arcsinx
du = (1)dx; v = 1/_/1 - x^2
du = dx; v = 1/_/1 - x^2

General formula of integrating by parts: uv - § vdu
x.1/_/(1-x^2) - § 1/_/(1-x^2)

using the u-substitution for § 1/_/(1-x^2):
u = 1-x^2
du = -2x dx
-1/2du = dx

x/_/(1-x^2) - § 1/_/u.(-1/2) + c
factorise out the -1/2:
x/_/(1-x^2) + 1/2 § u^(-1/2) + c
x/_/(1-x^2) + 1/2 § u^1/2/1/2 + c
x/_/(1-x^2) + 1/2.u^1/2/1/2 + c
x/_/(1-x^2) + |x|^1/2 + c
...you have done a great job my brother...but where you put dv=arcsinx...v will be integration of arcsinx...which makes the question complex
Re: How To Calculate Quickly And Correctly In Mathematics by SirChides(m): 1:49pm On Sep 17, 2013
Calculusf(x):
...hmmm,no sir...try more sir...let me give you hint...use integration by parts...let u be arcsinx and v be x...
xarcsinx+root(1+x^2)+c
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 6:02pm On Sep 17, 2013
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Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 6:41pm On Sep 17, 2013
My question: An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
Re: How To Calculate Quickly And Correctly In Mathematics by lavosier: 10:19pm On Sep 17, 2013
Ortarico: My question: An empty pool being filled with water at a constant rate takes 8 hours to fill to 3/5 of its capacity. How much more time will it take to finish filling the pool?
3/5of pool takes 8hrs.1pool shud tke 8/(3/5)=40/3hrs..so 40/3hrs - 8hrs=5hrs 20mins..
Op m rite sha.
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 9:07am On Sep 18, 2013
lavosier:
3/5of pool takes 8hrs.1pool shud tke 8/(3/5)=40/3hrs..so 40/3hrs - 8hrs=5hrs 20mins..
Op m rite sha.

Bravo, you killed it boss!
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 1:01pm On Sep 18, 2013
Calculusf(x):
...you have done a great job my brother...but where you put dv=arcsinx...v will be integration of arcsinx...which makes the question complex

Ok, i've corrected myself by making dv = x, u = arcsinx
Got the answer to be: (x^2)arcsinx + |_/1-x^2)|^1/2 + c
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 1:42pm On Sep 19, 2013
lavosier:
(1/2)x^2arcsinx-(1/4)arcsinx+1/4xsqreroot of (1-x^2)+c..ope am crrect??
...maybe...but pls,try to solve any questions you can solve my great bro...we are here not to test anyone's knowledge but to brainstorm and help one another
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 1:43pm On Sep 19, 2013
Ortarico:

Ok, i've corrected myself by making dv = x, u = arcsinx
Got the answer to be: (x^2)arcsinx + |_/1-x^2)|^1/2 + c
...my oga at the top...u will still integrate the square root of (1-x^2)...
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 2:42pm On Sep 19, 2013
Pls,explain ur answer bro@lavosier.
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 11:58am On Sep 20, 2013
Calculusf(x):
...my oga at the top...u will still integrate the square root of (1-x^2)...

ok my prof, but I just saw that you've done the correction can't find it anymore oo
Re: How To Calculate Quickly And Correctly In Mathematics by Ortarico(m): 11:59am On Sep 20, 2013
Calculusf(x):
Pls,explain ur question bro@lavosier.

What is his question prof? Can't find it too!
Re: How To Calculate Quickly And Correctly In Mathematics by MrCalculus(m): 12:14pm On Sep 20, 2013
my profs i hail una ooooo
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 1:52pm On Sep 20, 2013
lavosier:
(1/2)x^2arcsinx-(1/4)arcsinx+1/4xsqreroot of (1-x^2)+c..ope am crrect??
...using integration by parts,u=arcsinx and dv=xdx...du=1/√1-x²...v=½x²...substitute that to the formula ∫udv=uv-∫vdu...by substituting to the r.h.s...½x²arcsinx-∫½x²/∫√1-x²...½x²arcsinx-½∫x²/√1-x²...EQUATION 1...to save space,taken the one with integral sign...½∫x²/√1-x².dx...if x=sin@...(i)...dx=cos@d@...½∫sin²@/√1-sin²@*cos@...½∫sin²@/√cos²@*cos@...½∫sin²@/cos@*cos@...½∫sin²@d@...{from trigonometry,cos2@=1-2sin²@...sin²@=(1-cos2@)/2}...½∫(1-cos2@)/2...¼∫1-cos2@...¼(@-sin2@/2)...{from trigonometry,sin2@=2sin@cos@}...¼(@-sin@cos@)...from...(i)...x=sin@...@=arcsinx...cos@=√1-x²...substitute those to get...¼(arcsinx-x√1-x²)...EQUATION 2(don't forget we solved ½∫x²/√1-x²).then substitute it to equation 1 above to give...½x²arcsinx-¼(arcsinx-x√1-x²)...½x²arcsinx-¼arcsinx+¼x√1-x²...
Re: How To Calculate Quickly And Correctly In Mathematics by Calculusfx: 8:42pm On Sep 22, 2013
The are some numbers that there factors expect themselves are added up to them...e.g...6 with factors 1,2,3 and 6...without 6,the others are added to 6.....then 28 with factors 1,2,4,7,14and28,without 28...the others are added to 28...find the fifth number that can exhibit this
Re: How To Calculate Quickly And Correctly In Mathematics by MrCalculus(m): 1:13pm On Sep 24, 2013
Calculusf(x):
The are some numbers that there factors expect themselves are added up to them...e.g...6 with factors 1,2,3 and 6...without 6,the others are added to 6.....then 28 with factors 1,2,4,7,14and28,without 28...the others are added to 28...find the fifth number that can exhibit this
TH are prime _actors..
use 4mula:: 2^(p-1)*(2p-1).to get them
p=prime number

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