HELP Integral

[xiaa]

But I'm pretty new to calculus and I'm trying to teach myself how to do an integral because my math teacher confused the hell out of me the other day.

Comments

[joshua_green]

You could always expand the polynomial before integrating.
You erred when you just replaced the dx by du.  The original integral has dx and, since u = 1 - 3x, du/dx = -3, so dx = -du/3.

[joshua_green]

Therefore, you shouldn't get 2∫u2du, but should instead get 2∫u2(-du/3)

[xiaa]

So, I can't change the dx to a du, so I do it like this?

[joshua_green]

Yes, that's all true, though I would think that you'd rather convert everything to u's (your final expression is exactly what you began with).

[anonymous]

I found your problem..I think.

In order for you to substitute your integral into the "u^n du" form, here you set du equal to -3dx, which is correct but.. in making the substitution work, you've altered the value of the integral, so you have to divide by -3 outside the integral too so that you're really just multiplying by 1.

Hopefully someone else can leave you an answer that's more comprehensive.