Review for the Quiz 2 Math202 LM SP2014 1. Compute each of the following integrals. !
2
a) " sin 2 x!cos 2 x!dx b) " ln(2x + 1)dx
0
x2
1
c) "
dx
d)
" x 2 x 2 + 4 dx
(x # 3)(x + 2)2
e) " x
!
3
!
6
f ) " sin 2 (2x)dx
9 # x dx
3
2
x 2 + 11x
g) " e sin(2x)dx h) "
dx
(x # 1)(x + 1)2
#x
4 + x2
3x 3
i) "
dx j) "
dx
2
x2
9#x
2
x +1
k) " x 2 lnx!dx l) "
dx
1
1 + 4x 2
1
x3
x
m) " e dx n) "
!dx o) "
!dx
x + 4x 2
x2 # 4
2. Evaluate each of the following Integrals: a)
b) "
c) # 2xe! x !dx
2
1
d) #
!1
!2
e) ex
dx f ) "
!1 e x ! 1
1
1
(x + 1)
4
!dx
3
3. Compute each of the following limits (6+2 =8 points): a)lim(1" 2x)
1
2
x!0
b)lim
x!
#
2
1" sin $
csc$
c)lim(cos x)
3
x2
x!0
d)lim(sec x " tan x) x!
#
2
e)limx 3e" x
x!%
f )limx x
2
x!0 "
4. Use midpoint, trapezoidal and Simpson’s rule to approximate subintervals. The integral must be computed completely for full credit. From The Previous Final: Spring 2013: 1(a‐b), 2(a‐d), 7(b), 8(a‐b), 11(a); Fall 2012: 2(a‐d), 3(a‐b), 8 (a‐b); Spring 2011: 1, 3(a‐f), 7(a‐b), 8(b); Fall 2010: 2(a‐e), 3(a‐b), 8(a‐b); Spring 2009: 2(a‐e), 3(a‐b), 9(b), 10(b); using 4