Let and and you should get:
And since we're dealing with a definite integral, it doesn't matter that we ended up with u's.
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).
And for this problem, I don't even have the answer in the back of my book! Someone please help!
(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!
Thanks in advance!
Since it's a definite integral, you ultimately wind up plugging the limits into the antiderivative. So it doesn't matter if you start with x or u, as whichever variable you use will be replaced by the limits 0 and 1 anyway.
If you aren't buying it, just take your favorite definite integral and change the variable. You should get the same answer.