Math 106 BC Quiz 04 page 1 10/15/2010 Name
Circle your Section: B (11am) C (noon)
1. Find Z(cos x)5dx.
Note there is an odd number of factors of cos xhere, so use an appropriate substitution (such as u= sin x,u= sec x,
u= cos x,u= tan x, etc.) (do not use a “reduction formula”).
2A. Find Zdx
x6√x2
−16 by introducing an appropriate trig substitution.
Hint: it’s probably one of these: x= 4 sin t,x= 4 sec t, or x= 4 tan t.
You may find your answer in (1) above useful midway through this problem.
2B. Suppose the integral in (2A) is given lower and upper limits of 8 and 9, respectively. What is the corresponding lower
limit on the new integral after you make the substitution x=...? Answer to 4 decimal places or in terms of radicals.