MTH 114 Study Guide - Final Guide: Farad, Product Rule, Johann Bernoulli
Document Summary
Problem: let f be cont anc nonnegative on [a,b] (0= a=b), and let r be region that is bounded above y= f(x), below by x-axis, and on sides by x=a and x=b. Find volume of solid of revolution that is generated by revolving region r about y axis. Cylindrical shell: solid enclosed by two concentric right circular cylinders. V=[area of cross section][height] => 2pi avg radheightthickness. Also: volume of solid of revolution generated by revolving region r about axis can be obtained by integrating area of surface generated by arbitrary cross section of r taken parallel to axis of revolution. Problem: suppose y=f (x) is smooth curve on int [a,b]/is cont. Define and find formula for arc length l of curve y=f(x) over int (a,b) If y=f(x) is smooth curve on int [a,b], then arc length l of curve over [a,b] is l = integral from a to b of {1+[f"(x)]^2}^0. 5 dx.
