# Thread: 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.
$\displaystyle \int (81 - 0.1Q)^{\frac{1}{2}} \, dQ$

$\displaystyle u = 81 - 0.1Q$

$\displaystyle du = -0.1 \, dQ$

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

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

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

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

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 ?