MATH 101 Lecture 9: Areas and Volumes
Document Summary
So far we have used integration to find areas. Suppose now that we have a solid object and that. A(x) gives us the area of cross-section of the object at point, we can proceed to find its volume. Find the volume of a right-circular cylinder of length 4m and radius 1m. First we must sketch a cylinder so that its central axis is the x-axis. Make the other end touch the y-axis which would make any cross-section a circle of radius 1m. We are also concerned with volumes of revolution/rotation around given lines. Find the volume of the solid obtained by rotating about the x-axis, the graph of between x = 0 and 4 f (x)=0. 5x +1 f (x) 2= . The volume of a solid rotated about the x-axis is . If the solid is rotated about the y-axis: a b.
