Integral

VinnyJ · #1 $Old$ December 1st, 2008, 06:42 AM

I need help finding the Integer of x * (x-2)^7.
I don't understand why I can't figure it out my self because it doesn't seem that difficult. It is for finding the area under the graph between 0 and 2, i keep finding a different answer than that to my calculator gives me. I welcome any help anybody can give me.
thanks

Inti · #2 $Old$ December 1st, 2008, 07:23 AM

That integral has a little trick: the difficulty is that you have $(x-2)^7$ , which might be difficult to integrate, so do this:
Perform the change of variables $u=x-2$ and you will transform your integral into $\int_{-2}^{0} (u+2)u^7 du = \int_{-2}^{0} u^8+2u^7 du$ which is much more workable...

(I´m assuming that you wanted to get the integral between 0 and 2).