₦airaland Forum

You will recieve 2k worth of airtime if you get these questions within 5hrs

1. integral[1/((e^t)-1)]dt

2. integral(lnx)

3. show that |n|n-1=π/sinnπ (| rep a sign in gamma and beta function)

4. show that beta(m,n)=(|p|q)/|(p+q)

U dey find person wey go solve your assignment for you abi.. No worry...

Things will be made easy soon for you

sopstan:
You will recieve 2k worth of airtime if you get these questions within 5hrs

1. integral[1/((e^t)-1)]dt

2. integral(lnx)

3. show that |n|n-1=π/sinnπ (| rep a sign in alpha and beta function)

4. show that beta(m,n)=(|p|q)/|(p+q)

I'll pay you double that amount if you'll solve it.

ok after 5hrs...

Abeg keep your card

presh2dk:
Abeg keep your card

you've tried your best right?... e pain am

you've tried your best right?... ; e pain am

Simple.

Answer - South Africa.

where my card?

sopstan:
You will recieve 2k worth of airtime if you get these questions within 5hrs

1. integral[1/((e^t)-1)]dt

2. integral(lnx)

3. show that |n|n-1=π/sinnπ (| rep a sign in alpha and beta function)

4. show that beta(m,n)=(|p|q)/|(p+q)

sopstan:
You will recieve 2k worth of airtime if you get these questions within 5hrs

1. integral[1/((e^t)-1)]dt

2. integral(lnx)

3. show that |n|n-1=π/sinnπ (| rep a sign in alpha and beta function)

4. show that beta(m,n)=(|p|q)/|(p+q)

this resembles Mathematical Physics.. Beta and Gamma functions (Euler's function)

dejt4u:
this resembles Mathematical Physics.. Beta and Gamma functions (Euler's function)

something like that

MAKE I SOLVE

sopstan:
You will recieve 2k worth of airtime if you get these questions within 5hrs

1. integral[1/((e^t)-1)]dt

2. integral(lnx)

3. show that |n|n-1=π/sinnπ (| rep a sign in alpha and beta function)

4. show that beta(m,n)=(|p|q)/|(p+q)

2. sol integral(Inx)= integral(lnx.x°) (where x°=1)

this becomes integral(udv)

u=Inx and dv=x°

du=1/x and v=x then using integratn by parts

you have uv-integral(vdu) which will be

Inx.x-integral(x.1/x)dx = xInx-x = x(Inx-1)ans...

It's like you don't know where to post such question. Nairaland is characterized by lazy men and women

sopstan:
You will recieve 2k worth of airtime if you get these questions within 5hrs

1. integral[1/((e^t)-1)]dt

2. integral(lnx)

3. show that |n|n-1=π/sinnπ (| rep a sign in alpha and beta function)

4. show that beta(m,n)=(|p|q)/|(p+q)

1. sol integral[1/((e^t)-1)]dt
u=e^t, du=e^tdt, dt=du/e^t=du/u
the whole guy now becomes integral[du/u(u-1)]
then you resolve into partial fraction it now becomes
integral[1/(u+1)-1/u]du you then integrate=
In(u+1)-Inu=In[(u+1)/u] (since u=e^t) the whole guy now becomes
In[((e^t)+1)/e^t] or In[1+1/e^t]ans...
now do the rest

Mrkumareze:
It's like you don't know where to post such question. Nairaland is characterized by lazy men and women

like seriously?

3).
Another common integral representation of the beta function is
B( x , y ) = ∫ ∞ 0 t x −1

(1 + t ) x + y dt .

So

Γ( n)Γ(n-1) = B( n, n − 1) = ∫ ∞ 0 t n −1

1 + t dt .

That integral can be evaluated by considering
f( z ) = z n −1
1 + z and integrating around a keyhole contour with the branch cut for z n-1 along the positive real axis.
Then
∫ ∞ 0 t n−1
1 + t dt + ∫ 0 ∞ ( te 2 πi ) n −1
1 + t dt = 2 πi Res[ f ( z ),
= 2 πi ( e πi ) n −
= − 2 πie πin
which implies
∫ ∞ 0 t n −1
1 + t dt = −2 πie πin
1 − e 2 πin
= π 2 i
e πin − e − πin

= π
sinπn

BunbleBee:
3).
Another common integral representation of the beta function is
B( x , y ) = ∫ ∞ 0 t x −1

(1 + t ) x + y dt .

So

Γ( n)Γ(n-1) = B( n, n − 1) = ∫ ∞ 0 t n −1

1 + t dt .

That integral can be evaluated by considering
f( z ) = z n −1
1 + z and integrating around a keyhole contour with the branch cut for z n-1 along the positive real axis.
Then
∫ ∞ 0 t n−1
1 + t dt + ∫ 0 ∞ ( te 2 πi ) n −1
1 + t dt = 2 πi Res[ f ( z ),
= 2 πi ( e πi ) n −
= − 2 πie πin
which implies
∫ ∞ 0 t n −1
1 + t dt = −2 πie πin
1 − e 2 πin
= π 2 i
e πin − e − πin

= π
sinπn

the integral limit should be 0-1 since it's a beta function B(m,n) you try weldone

.

sopstan:
You will recieve 2k worth of airtime if you get these questions within 5hrs

1. integral[1/((e^t)-1)]dt

2. integral(lnx)

3. show that |n|n-1=π/sinnπ (| rep a sign in alpha and beta function)

4. show that beta(m,n)=(|p|q)/|(p+q)

I can solve it for you. I am not with my android phone here, but I'l send it in the evening when I get back home. Please kindly send your whatsap number to praisejummy42@gmail.com

which you championed

Mrkumareze:
It's like you don't know where to post such question. Nairaland is characterized by lazy men and women

Anus ofcourse

sopstan:
we're talking maths here this one is talking trash pls where do you think from