# Thread: Help with integration

1. ## Help with integration

Hey this is a calculus problem although its for probability i finished calc 3 like 2 years ago and forgot how to integrate. Teacher doesn't make us integrate anything difficult on test questions but hw loves to give us funky pdf's to integrate to get to marginals and stuff.

Integral from 0-1 (y) * (n) * (1-y)^(n-1) dy

I think the answer is 1/(n+1) based on the problem i just dont know how to integrate it i tried parts and got nowhere maybe im missing an easy simplification step somewhere

2. have you ever covered the Beta function?

3. no is that a probability function?

4. Originally Posted by ChrisBickle
Hey this is a calculus problem although its for probability i finished calc 3 like 2 years ago and forgot how to integrate. Teacher doesn't make us integrate anything difficult on test questions but hw loves to give us funky pdf's to integrate to get to marginals and stuff.

Integral from 0-1 (y) * (n) * (1-y)^(n-1) dy

I think the answer is 1/(n+1) based on the problem i just dont know how to integrate it i tried parts and got nowhere maybe im missing an easy simplification step somewhere
That's $\displaystyle \int_0^1 n y(1- y)^{n-1}dy$?

Let u= 1- y so du= -dy, y= 1- u and when y= 0, u= 1, when y= 1, u= 0. The integral becomes $\displaystyle -n\int_1^0 (1-u)u^{n-1}du= \int_0^1 u^{n-1}- u^n du$

While that is the beta function B(2, n), it is a very simple case.

5. you misread it, it's actually $\displaystyle y^n.$