1. CHAPTER 2 2.4 Continuity Volumes Definition of Volume: Let S be a solid that lies between x = a and x = b. If the cross-sectional area of S in the plane P x,through x and perpendicular to the x-axis, is A(x), where A is a continuous function, then the volume of S is V = lim n ->   A(x i * )  x =  a b A(x) dx.

2. Example: Find the volume of the solid. y = e x, y = 0, x = 0, x = 1; about the x-axis. Example: Find the volume of the solid. y=cos x, y=sin x, x=0, x=  /4; about the x-axis. Example: Find the volume of the solid. y= x, y=0, x=2, x=1; about x=1.

3. CHAPTER 2 2.4 Continuity 1. A right circular cone with height h and base radius r. Example: Find the volume of the described solid S. 2. A frustum of a pyramid with square base of side b, square top of side a, and height h.