The integral ##\int_a^b x\left(\frac{b-x}{b-a}\right)^{n-1} \; dx## can be effectively solved using the substitution ##u = b-x##. While an initial attempt with ##u = \frac{b-x}{b-a}## was made, it was clarified that the constant ##b-a## does not affect the substitution's validity. Both substitutions lead to the correct solution, demonstrating flexibility in approach.
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That substitution should work: show us what went wrong when you tried it.squenshl said: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.
Thanks a lot. I got it.Samy_A said: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.