Solve Integral: Tell if Hemisphere or Cone

[yaho8888]

Homework Statement

$$\int \pi (\frac{x}{3})^2 dx$$

how can you tell whather this equation is for hemisphere or cone.

no idea how to start.

 

[berkeman]

First, that is not an equation, it's an indefinite integral. Second, it is a fairly easy to solve integral. Third, it would appear to have nothing to do with the 3-dimensional mathematical description of either a hemisphere or a cone.

Could you please rephrase the question?

 

[Hurkyl]

It's not even an equation...

 

[HallsofIvy]

The "equation" isn't for either one! If the question is really what you say , it has nothing to do with a cone or a hemistpher. It's an integral! Knowing that the integral of x² is (1/3)x³ should make it easy!

 

[yaho8888]

it is an intergral for finding the volume of a cone or a hemistpher.
forgot from 0 to 12.

 

[yaho8888]

any one knows

 

[HallsofIvy]

Any one knows WHAT? What question are you asking? An integral is an integral. You can get exactly the same integral for different applications.

Typically to find volume you have to integrate some kind of area. Looks to me like (x/3) is some kind of radius (so that $pi (x/3)^2$ is the area of a circle). In other words, it looks like you are doing a volume of rotation. But then the radius is a LINEAR function of x- the part that being rotated is a straight line: okay is that a cone or a sphere?