February 7, 2006
Lecturer: Dr Martin Kurth
Hilary Term 2006
Course 1E1 2005-2006 (JF Engineers & JF MSISS & JF MEMS)
Problem Sheet 4
Due: in the Tutorials 17 February / 20 February
To demonstrate a theorem, it is neither necessary nor even advantageous to
know what it means.
Jules Henri Poincaré (1854–1912)
1. Calculate the volume of the solid generated by revolving the area between
the x-axis and the graph of the function f with
f (x) = 1 − x2
about the line x = −2.
(5 points)
2. Calculate the length of the graph of
f (x) = x2/3
between x = 1 and x = 8.
(5 points)
3. Show that the shortest smooth curve connecting two points (x1 , y1 ) and
(x2 , y2 ) is a straight line.
(*)
Questions 1 and 2 should be answered by all students, you will get points for them. Question 3
is more challenging and meant as an exercise for the more mathematically interested students.