Calculus 081b, 2005: Solutions to Part B of Midterm Exam
Problem 26.
/4
Evaluate
x tan x sec2 x dx
0
There were at least ve or six dierent ways to do this. We show two solutions. First, note that this is
proper, i.e. not improper, because x tan x is well
CALCULUS 081A, QUIZ 3 SOLUTIONS
Part A: Multiple Choice Questions
For each question circle the correct answer and mark it in the SCANTRON sheet, if available. Full solution is not required for the questions in
this part and will not be taken into account
Calculus 081B Quiz #2 Solutions
B. Chorny
1.
2.
sin x
cos x tan x dx = cos x cos x dx = sin x dx = cos x + C
0
2
sin x cos(cos x )dx
Let u = cos x
du = sin xdx
If x = 0 then u = 1
If x = then u = 0
2
= cos u du
0
1
= [sin u ] 1
0
= sin 0 + sin 1
= sin 1