i have to show that:(adsbygoogle = window.adsbygoogle || []).push({});

1)[tex](-1)^n\int_{-1}^{1}(x^2-1)^ndx=2^{2n+1}(n!)^2/(2n+1)![/tex]

2) [tex]\binom{n}{k}=[(n+1)\int_{0}^{1}x^k(1-x)^{n-k}dx]^{-1}[/tex]

for the first part i thought to use newton's binomial, i.e:

[tex](1-x^2)^n=\sum_{k=0}^{n}\binom{n}{k}(-x^2)^k[/tex]

but it didn't get me far.

for the second part i dont have a clue, i dont think you can integrate the integral by parts or substitution can you?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Technical question on integrals.

**Physics Forums | Science Articles, Homework Help, Discussion**