# Calculus substitution

• Apr 30th 2007, 03:08 PM
UMStudent
Calculus substitution
Alright I have a review questions I need help on for this upcoming test. So any help will greatly be appreciated and I'm sure provide to me getting an A on my next test which I surely need.

Show that one of the substitutions u = e^3x, v = x-3, w= cos(3x) can be used to find an explicit antiderivative of x*sqrt(x-3). Find an explicted expression for integral x*(x-3) dx.

Again thanks.
• Apr 30th 2007, 09:12 PM
ecMathGeek
Quote:

Originally Posted by UMStudent
Alright I have a review questions I need help on for this upcoming test. So any help will greatly be appreciated and I'm sure provide to me getting an A on my next test which I surely need.

Show that one of the substitutions u = e^3x, v = x-3, w= cos(3x) can be used to find an explicit antiderivative of x*sqrt(x-3). Find an explicted expression for integral x*(x-3) dx.

Again thanks.

It appears to me the u and w substitutions won't do you much good (u might, but it seems a bit too complicated to try). The v substitution is the obvious one to work.

INT x*sqrt(x - 3) dx

Let v = x - 3 --> x = v + 3 <--> dx = dv

INT (v + 3)*sqrt(v) dv
= INT v*sqrt(v) + 3*sqrt(v) dv
= INT v^(3/2) + 3v^(1/2) dv
= 2/5*v^(5/2) + 2v^(3/2) + C

As for your second problem, x*(x-3) dx, no substitution is needed. Check to make sure this is the correct problem.
• Apr 30th 2007, 09:16 PM
Jhevon
Quote:

Originally Posted by ecMathGeek

As for your second problem, x*(x-3) dx, no substitution is needed. Check to make sure this is the correct problem.

i think he was refering to the same question, x*sqrt(x - 3), in which case you already answered the question
• May 1st 2007, 06:26 AM
UMStudent
Yes the x*x-3 was just a typo I left out the sqrt. Thanks for your help and yes I did erase the first problem found i similiar problem I as able to work with.