January 17, 2005
Lecturer: Dr Martin Kurth
Hilary Term 2006
Course 1E1 2005-2006 (JF Engineers & JF MSISS & JF MEMS)
Problem Sheet 1
Due: in the Tutorials January 27 / January 30
. . . the referee is informed before any proposed substitution is made.
from: FIFA Laws of the Game
1. Calculate the following indefinite integrals, using the given substitutions.
R
(a) (x + 2)2 dx,
u = x + 2,
R
2
(b) x sin(3x )dx,
u = 3x2 .
(4 points)
2. Calculate the following indefinite integrals:
R
(a) x(x2 + 1)3 dx,
R
√
(b) √1x cos( x)dx,
R
(c) cos2x(x2 ) dx.
3. What is
Z
(6 points)
6 tan2 x
dx?
(cos2 x)(3 + tan3 x)2
(*)
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.