Math 106-01: Calculus II: Reading Homework 8.1

1. Applications to Geometry : how may a quantity be expressed as a definite integral? how does this work when approximating distance travelled? what does the dt represent in the integral?
   
   1. Computing Volumes or Lengths : how do we calculate the volume or length of a solid or curve?
      
      1. computing volumes : how do we chop a cone to approximate its volume with a definite integral? why? how are the limits of an integral for a volume determined?
         
      2. more volumes : how is the integral for the region bounded by the curves y=x and y=x² rotated around the line y=3 different from the other examples in the section?
         
   2. Arc Length : how do we find the arc length ofa curve y=f(x)?