Math 2260 Final Exam Practice Problem Solutions1. Write down an integral which will compute the length of the part ofy= lnxfor 1≤x≤2. Don’tworry about evaluating this integral.2. LetV(a) be the volume obtained by rotating the area between thex-axis and the graph ofy=1x3/2fromx=atox= 1 around they-axis. What happens asagoes to zero?3. What is the volume of the solid obtained by rotating the part of the graph ofy= cosx√sinxbetweenx= 0 andx=π/2 around thex-axis?1
4. Find the volume obtained by rotating the region between thex-axis, they-axis, and the linex+y= 1around the linex=-2.5. Calculate the surface area obtained by rotatingy=√xaround thex-axis for 3/4≤x≤15/4.6.(a) Find the area betweeny= 3 sin(πx) andy= 6xforx >0.0.20.40.60.81.01234562
(b) What is the volume obtained by rotating this region around thex-axis?