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...

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?

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

Kudos to everybody here

Calculusf(x):
Kudos to everybody here

I SIGHT U @D G.THREAD BRO.
KUDOZ!!

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!

Morning to all my generals...

....Integrate xarcsinx.dx....

Calculusf(x):
....Integrate xarcsinx.dx....

i think datz x/root(1-x^2) -root(1-x^2)+c

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...

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...

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??

.

.

^ thanks to my star. Alas, got posted!

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.

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

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

.

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?

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.

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!

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

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

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)...

Pls,explain ur answer bro@lavosier.

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

Calculusf(x):
Pls,explain ur question bro@lavosier.

What is his question prof? Can't find it too!

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...

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

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