Math Help - Need help with Consumer Surplus and the Integration step (easy)

1. Need help with Consumer Surplus and the Integration step (easy)

Im doing online homework of consumer surpluses and the example gives a step that is the integration part that I don't understand. it goes from squareroot(81-.1q) -8 dq and this is what you get when you integrate -20/3 (81-.1q) ^3/2 -8q My question is how do you get the -20/3 in front? Where does that come from? Hopefully you understand the different steps.

2. Originally Posted by tim
Im doing online homework of consumer surpluses and the example gives a step that is the integration part that I don't understand. it goes from squareroot(81-.1q) -8 dq and this is what you get when you integrate -20/3 (81-.1q) ^3/2 -8q My question is how do you get the -20/3 in front? Where does that come from? Hopefully you understand the different steps.
$\int (81 - 0.1Q)^{\frac{1}{2}} \, dQ$

$u = 81 - 0.1Q$

$du = -0.1 \, dQ$

$\textcolor{red}{-10} \int (81 - 0.1Q)^{\frac{1}{2}} \, \textcolor{red}{(-0.1)} \, dQ$

$-10 \int u^{\frac{1}{2}} \, du$

$-10 \cdot \frac{2}{3} u^{\frac{3}{2}} + C$

$-\frac{20}{3} (81-0.1Q)^{\frac{3}{2}} + C$

3. What if instead of -.1 the number was -.13? What would the -10 change to? Thanks for your help skeeter!!!!

4. Originally Posted by tim
What if instead of -.1 the number was -.13? What would the -10 change to? Thanks for your help skeeter!!!!
what is the relationship between -0.1 and -10 ?