MA 1023 LAB 1 A'97
IMPROPER INTEGRALS and INFINITE SERIES
Before solving the exercises from today's lab, you should copy in your home-directory a MAPLE file by using the following command:
cp ~/vernescu/Mlab1.mws ~;
The file contains some examples with sequences, visualization of sequences and series. This should complement the information and examples that you already have in the file Maple.mws that you copied last week.
You can then start the Maple engine by using the xmaple command. Click on FILE and OPEN Mlab1.mws. Read the examples and work some of your own. Once you feel confortable with the commands, you can try to solve the following exercises. You have to create your own MAPLE file and attach a printout to your report.
(i) Find the area of the region bounded between , the positive x-axis, x=1 and .
(ii) Find the volume of the solid of obtained by revolving the curve about the x-axis, between x=1 and .
(iii) Find the area of the surface generated by revolving about the x-axis between x=1 and .
(iv) Give the range of values of p > 0 for which your answers to the above 3 problems are finite. Is there any relationship between the three quantities. (The formula for area of surface of revolution may be found on p. 400 of the text.)