Need help with this question:

[Calculus Help]

What is the exact volume of a solid that is formed with a square base, aligned with the center of the solid on the x-axis and the edge of the base following the function f(x)= (1/5)x on the interval [0, 6]. I'm supposed to use volume by integration but have no idea how to do this problem.

 

[tkhunny]

You draw little squares along the x-axis and add up all their areas.

The first square is 0 x 0 at the Origin.
The last square is 12/5 x 12/5 at x = 6.

Does adding up REALLY SKINNY squares to create a solid remind you if anything? Maybe an Integral?

 

[Steven G]

Given any height between 0 and 6 what are the measurements of the sides of the square? Then what is the area of the square? The areas of these squares are what you want to add up.