# Calculus : U-Substitution

• Dec 9th 2008, 05:35 PM
Afterme
Calculus : U-Substitution
The problem is x(16-3x)^1/2 dx

u = 16 - 3x
du = -3 dx

My problem is how do I get rid of the X in the original problem? I can divide -1/3 to get rid of the -3 and that'll take care of the dx but as for the X I have no idea how to go about it. Help =)
• Dec 9th 2008, 05:42 PM
skeeter
Quote:

Originally Posted by Afterme
The problem is x(16-3x)^1/2 dx

u = 16 - 3x
du = -3 dx

My problem is how do I get rid of the X in the original problem? I can divide -1/3 to get rid of the -3 and that'll take care of the dx but as for the X I have no idea how to go about it. Help =)

$\displaystyle u = 16-3x$

$\displaystyle 3x = 16-u$

$\displaystyle x = \frac{1}{3}(16-u)$

substitute ...

$\displaystyle \int \frac{1}{3}(16-u) \cdot u^{\frac{1}{2}} \cdot \frac{du}{-3}$

$\displaystyle -\frac{1}{9} \int 16u^{\frac{1}{2}} - u^{\frac{3}{2}} \, du$
• Dec 9th 2008, 06:06 PM
Afterme
Quote:

Originally Posted by skeeter
$\displaystyle u = 16-3x$

$\displaystyle 3x = 16-u$

$\displaystyle x = \frac{1}{3}(16-u)$

substitute ...

$\displaystyle \int \frac{1}{3}(16-u) \cdot u^{\frac{1}{2}} \cdot \frac{du}{-3}$

$\displaystyle -\frac{1}{9} \int 16u^{\frac{1}{2}} - u^{\frac{3}{2}} \, du$

Thanks alot =)
• Dec 9th 2008, 06:10 PM
skeeter
distributive property of multiplication ...

$\displaystyle (16 - u)u^{\frac{1}{2}} = 16 \cdot u^{\frac{1}{2}} - u \cdot u^{\frac{1}{2}} = 16u^{\frac{1}{2}} - u^{\frac{3}{2}}$