Question

Beta Function...
Please Help :)

Answer 1

\[\rm \int\limits_{0}^{1}\frac{ x^2 }{\sqrt{1-x^4} }\int\limits_{0}^{1}\frac{ dx }{\sqrt{1-x^4} }dx\]


\(\rm Put~x^4=t~\\~at~ the~ end~ i~ get~ this~\[\frac{1}{4} \beta(\frac{1}{4},\frac{1}{2}) \cdot~\frac{1}{4} \beta(\frac{3}{4},\frac{1}{2})\]\)

Answer 2

after evaluating further
i get the following :
\[\frac{ 1 }{ 16 }\cdot~\frac{\Gamma3/4\cdot~\Gamma 1/2 }{ \Gamma 5/4} \cdot~\frac{\Gamma1/4\cdot~\Gamma 1/2 }{ \Gamma 3/4 } \]

Answer 3

the ans must equal to : \[\frac{ \pi }{ 4\sqrt{2} }\]

Answer 4

im not getting the final ans :(

Answer 5

@ganeshie8 @Kainui @zzr0ck3r

Answer 6

there is only one dx XD

Answer 7

@mathmale @baru

Answer 8

im getting \(\pi \sqrt 2\)/4

Answer 9

Wolfram Alpha shows a different result.

Answer 10

its a prove type question

Answer 11

I'm new to this sort of thing, but y did you choose t to equal x^4?

Answer 12

to get the standard form

Answer 13

If you show your steps perhaps I can see what went wrong.

Answer 14

well wait
ill post it on pa

Answer 15

PA?

Answer 16

haha
nothing
:)

Answer 17

How are you using the Beta function with two integral functions of x?

Answer 18

well what i noticed we could club both
leading to a single integral XD

Answer 19

Can you rewrite your product as a ratio of integrals?