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

  1. #1
    tim
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    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.
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    Quote Originally Posted by tim View Post
    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
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  3. #3
    tim
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    What if instead of -.1 the number was -.13? What would the -10 change to? Thanks for your help skeeter!!!!
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    Quote Originally Posted by tim View Post
    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 ?
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