# Homework Help: Intervals on an integral

1. Feb 4, 2012

### bobsmith76

1. The problem statement, all variables and given/known data

I understand about everything except why the b and a values on the integral change from 0,3 to 9,36

2. Feb 4, 2012

### tiny-tim

hi bobsmith76!

09 dx is an abbreviation for ∫x=0x=9 dx …

now convert x to u !

3. Feb 4, 2012

### bobsmith76

I know what it's an abbreviation for but how do you go from 0,3 to 9,36 by what rule is that legal?

4. Feb 4, 2012

### tiny-tim

uhh?

u = x3 + 9

so x = 0 -> u = 9,

so x = 3 -> u = 36

5. Feb 4, 2012

ok, thanks

6. Feb 4, 2012

### bobsmith76

Does this rule have a name so that I can look it up in my book? I don't see why u-substitution should be related to the a and b values on an integral.

7. Feb 4, 2012

### Dick

I don't think it has any particular name. But if you express your final integral as a function of u, then the limits have to change to the limits for u. If you don't like that, then change the u back into x^3+9 at the end, so you've got 6π(x^3+9)^(1/2). Now use the original limits. It's exactly the same thing.

8. Feb 5, 2012

### tiny-tim

(just got up :zzz: …)
yes … and the name is u-substitution!

if you substitute u for x, you must do so wherever x occurs,

including in the the limits!!

u-substitution does exactly what it says on the tin!