Friday, 12 February
Math 105, section 207
Quiz 5
Name:
Student number:
Time: 13 minutes
1. Compute the region between the graph of y = 3x−6 and the x-axis, for 0 ≤ x ≤ 6:
a)30
b)18
c)12
d)96
2. (Midterm 2 Sample 3) Compute the Midpoint Riemann sum for the function
f (x) = x2 on the interval [−5, 5] using n = 5 equal subintervals?
a)130
b)90
c)80
d)40
R √3
1
dx?
1 + x2
π
π
π
π
a)
b)
c)
d)
12
4
3
2
Rx
4. Let F (x) = 0 tan t dt. What is the derivative of G(x) = F (x2 )?
a)tan(x2 )
b)1 + tan2 (x2 )
c)2x(1 + tan2 (x2 ))
d) 2xtan(x2 )
3.
1
Rπ
5. Evaluate 04 sin x cos x dx:
a) 41
b) 12
c) −1
d) 34
4
R
6. cos3 x dx?
a) 41 cos4 x + C
b)− 14 sin4 x + C
7.
π
4
sec2 x tan1/2 x dx
a)
b) 32
R
0
2 3/2
3π
c) 12 π 2
d) −1
3
c)sin x − 13 sin3 x + C
d)cos 4x + C
Friday, 12 February
Math 105, section 207
Quiz 5
Some formulae:
1 + cos2x
1 − cos2x
, sin2 x =
,
2
2
1
1
secx =
, (tanx)0 = 1 + tan2 x =
= sec2 x,
cosx
cos2 x
Z
Z
tanx dx = −ln|cos x| + C = ln|sec x| + C,
cotx dx = ln|sinx| + C,
cos2 x =
Z
Z
secx dx = ln|secx + tanx| + C,
cscx dx = −ln|cscx + cotx| + C,
1 − sin2 x = cos2 x,
1 + tan2 (x) = sec2 x,
sec2 (x) − 1 = tan2 x,
sin2x = 2sinx cosx,
cos2x = cos2 x − sin2 x = 2cos2 x − 1 = 1 − 2sin2 x