# Another "theoretical" thing about integrals I have no idea how to do

• February 6th 2010, 11:48 AM
s3a
Another "theoretical" thing about integrals I have no idea how to do
Question:
If a and b are positive numbers, show that

this(integral (x^a * (1-x)^b) from 0 to 1) = this(http://www.wolframalpha.com/input/?i=integral+(x^b+*+(1-x)^a)+from+0+to+1).

(Ignore what Wolfram Alpha says - I am just using those links to make it more visual because I don't know how to use latex)

Any help would be GREATLY appreciated!
Let $u = 1-x$ and $du = -dx$ and you should get:
$\int_0^1 x^a (1-x)^b dx = -\int_1^0 (1-u)^a u^b du = \int_0^1 (1-u)^a u^b du$