Calculating Integral: ##\int_a^b x\left(\frac{b-x}{b-a}\right)^{n-1} \; dx##

[squenshl]

Homework Statement

How do I calculate $\int_a^b x\left(\frac{b-x}{b-a}\right)^{n-1} \; dx$?

Homework Equations

The Attempt at a Solution

I tried the substitution $u = \frac{b-x}{b-a}$ to no avail. Someone please help.

 

[Samy_A]

Homework Statement

How do I calculate $\int_a^b x\left(\frac{b-x}{b-a}\right)^{n-1} \; dx$?

Homework Equations

The Attempt at a Solution

I tried the substitution $u = \frac{b-x}{b-a}$ to no avail. Someone please help.

That substitution should work: show us what went wrong when you tried it.
A little hint: don't bother with the $b-a$ in the denominator, as that is a constant. Set $u=b-x$.
EDIT: it doesn't really matter, both substitutions work just fine.

 

[squenshl]

That substitution should work: show us what went wrong when you tried it.
A little hint: don't bother with the $b-a$ in the denominator, as that is a constant. Set $u=b-x$.
EDIT: it doesn't really matter, both substitutions work just fine.

Thanks a lot. I got it.