Help with activity (parabolic container filled with water, y = x^2/2, 0<=x<=2)

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armn91

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Hello all, I am trying to complete this activity, but I get stuck. Could anyone be so kind and help me out? Thank you very much.
 

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armn91 said:
What are the limits of integration, volume and distance?
Click to expand...
If the origin was at the top of the water, then I would move the origin down 2 units and be back at the original problem and solve that one. If you insist on not moving the origin, then you need to decide what the equation will be of the container, from which y values will each slab of water move from and to?
You need the EXACT same information that you needed to do the original problem.

Try to solve it, it will be fun. DRAW a diagram of the new setting!
 
Steven G said:
If the origin was at the top of the water, then I would move the origin down 2 units and be back at the original problem and solve that one. If you insist on not moving the origin, then you need to decide what the equation will be of the container, from which y values will each slab of water move from and to?
You need the EXACT same information that you needed to do the original problem.

Try to solve it, it will be fun. DRAW a diagram of the new setting!
Click to expand...
Thank you for the indications. I am not planning to move it but I am having a lot of trouble setting up the equation and limits of integration. Could you please give some ideas to start?
 
armn91 said:
What are the limits of integration, volume and distance?
Click to expand...
I asked you a question … the parabola function with vertex at the origin is [imath]y=\dfrac{x^2}{2}[/imath].
What is the new equation if the vertex is shifted down 2 units?
 
armn91 said:
Thank you for the indications. I am not planning to move it but I am having a lot of trouble setting up the equation and limits of integration. Could you please give some ideas to start?
Click to expand...
I did give you an idea on how to start. DRAW A DIAGRAM. In the original graph you were able to get the information that you needed to do the problem from the diagram. This same information will be in the new diagram.
I can't really help until you draw a diagram with some values on the x and y axes so we can talk about things intelligently,
 
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