Integral Issue (Y-Axis) Solve for Volume

In summary, the conversation is about solving for volume using the Y-axis as the integral issue. The problem involves finding the integral of 1/4 (19-y)^2 dy from 0 to 18 and using it to calculate the volume. The person is struggling with integrating the equation and is seeking help. The suggested solutions are to either foil out the expression or use substitution, and to recall the power antidifferentiation rule.
  • #1
1joey1
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Integral Issue (Y-Axis) Solve for Volume :)

Homework Statement


[PLAIN]http://img88.imageshack.us/img88/7091/unled4mo.jpg

Homework Equations



V=
pi [itex]\int[/itex] [itex]^{18}_{0}[/itex] 1/4 (19-y)[itex]^{2}[/itex]dy

The Attempt at a Solution



I've tried it a couple times, gotten 243/2 Pi




Any and all help would be much appreciated :)

I'm really having trouble integrating the equation above, I am absolutely terrible with integrals so any help with that would be ideal
 
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  • #2


There are two ways to integrate this (I'm not sure what would be easier for you). Try foiling out your expression or using a substitution. Can you be more specific as to what you are having trouble with?

You will certainly need to recall the power antidifferentiation rule for this problem.
 
  • #3

1. What does the Y-axis represent in the integral issue?

The Y-axis in this context represents the variable we are trying to solve for, which is typically volume. It is the dependent variable in the equation.

2. How is the Y-axis used to solve for volume in an integral?

The Y-axis is used to represent the height of the three-dimensional shape we are trying to find the volume of. By setting up an integral with the Y-axis as the variable of integration, we can find the volume under the curve.

3. What is the difference between an integral issue and a regular integral?

An integral issue is a specific type of integral where we are solving for a specific variable, such as volume, using the Y-axis as the variable of integration. Regular integrals can have any variable of integration and may solve for other quantities, such as area or distance.

4. Can the Y-axis be any other variable besides volume in an integral issue?

Yes, the Y-axis can represent any other dependent variable in an integral issue. For example, it could represent the height of a tank filled with water and we could use it to solve for the total amount of water in the tank.

5. How does the choice of Y-axis affect the outcome of an integral issue?

The choice of Y-axis can greatly affect the outcome of an integral issue. It determines what quantity we are solving for and the range of values that will be included in the integration. It is important to carefully choose the Y-axis to accurately represent the problem at hand.

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