Week in Review # 10
3
MATH 142
Section 6.4 6.5, 6.6
Drost-Spring 2014
Nov 17th, 2014
  5 x  3x  dx
2
0
6.5 Fundamental Theorem of Calculus
6.4 Definite Integrals
1.
7.
Find the exact value using geometry:
8.
9.
2.
Evaluate the definite integrals below given:
A  2.4, B  1.25, C  0.5, D  1.5
  4  32x  dx
 x 9  x dx
3
3
1
9
0
10. Find the exact value of

3
0
x
dx
4  x2
11. The Ringin’ Ringtone Company finds their
marginal cost is defined by C   x   200  2 x
y
where x is the number of ringtones produced each
month. Compute the increase in cost to change the
production level from 50 ringtones each month to
100 ringtones per month.
f(x
12. a. Write the integral to represent the area below
f(x) and above the x-axis when
−a
A
a
b
C
c
d
D
B
x
b. Sketch the graph.
c. Find the area.
d
a)

f ( x)dx
b)
a

 f ( x)dx
a
c
c)
6.6 Area Between Curves
c
d)
b

f ( x)dx
14.
d
Use the Properties of definite integrals, and
3
3
 x dx  9,
 x dx  63
0
0
3
2
to evaluate each of the following:
3.
 6x dx
0
3
4.
 4x
2
dx
2
dx
0
3
5.
 6x
6
 x dx  4.5,
3
3
2
g ( x)  2 x  16 .
b
f ( x)dx
13. Find the area bounded by f ( x)  x  1 and
2
and
 5x
6
2
dx
3
g ( x)  6 x  6 .
Find the area bounded by f ( x)  e
15.
x
and
g ( x)  x over the interval 3  x  5 .
16. The rate of production of oil from a producing
field is described by R  t  
50
 15 , on the
t  20
interval from 0 ≤ t ≤ 12 where R(t) is the rate of
production in thousands of barrels per year, t years
after pumping begins. Find the area between the
graph of R and the t axis over the interval [3,10], and
interpret the results.
Extra Practice
3
6.
Find the area bounded by f ( x)  x  7 x  6
17.

  ax
3
 bx 2 
c 
  dx
x2 x 
18.
 4t  e
19.
8 x3  12 x  6
dx

x2
20.
  9 x  27 
21.
  5  16 x  dx
t2
dt
b
3 x 2  18 x  6 dx
3
a
22. Using substitution, rewrite the following integral,
5
x
9  x dx , in terms of u, where u  9  x .
0
23.
 e
24. Given
2
dt
 f  x  dx  50 , and  f  x  dx  30 ,
5
5
2
3
find the area under the curve
 2,3 .
25.
 xe
3x 2
dx
f  x  over the interval