How much water is used when the water falls 1 cm from 100 to 99 cm?

[mimi.janson]

Homework Statement

Hi i need to use V'(h) to find out how many liter of water are used when the water falls 1 cm

c) from 100 to 99 cm

Homework Equations

I know that V'(h)=(∏*(h²)+212,6/6)+(∏*h²)/3

The Attempt at a Solution

I know that i need to solve the differential equation and integrate between the limits 100 and 99. I do know how to integrate between the given limits, but i don't understand what it means to solve the equation. I already have v(h) and did integrate it in a former question where i got V'(h) so does solving the equation means that i need to find V''(h) or what ?

i will be gratefull for help so please help me

 

[SteamKing]

Please use the Homework Template and furnish the complete text of the problem statement.

 

[HallsofIvy]

"Solve an equation" means to find an unknown that satisfies the equation! Here, the "unknown" is the function V(h). No, you do not want to find V'', you want to go the other way and find V itself.

For this situation, where the "differential equation" is "dV/dh= f(h)", you just need to find the anti-derivative of f.

 

[Ash L]

I agree with Steamking and HallsofIvy. Since I can't see the full version of your question, I will try and guess at it. From experience, I think V(h) represents the volume of water at height h. So, V'(h) is the flow rate of water going out. I think you're asked to find the difference in volume between the heights 100 to 99 which they called it "how much water has been used".

Then it would be (V(100) - V(99)) or (V(99) - V(100)) depending on your V(h) and other constraints in the question.