Math 142 In Class Exam 3 Review
1. Find each indefinite integral.
a)
c)
e)
x
2
3
4
( x  5 ) dx
12 x
2
 8x
 x 3  x 2  20
 ( x  5)
2
b)
dx
 (x

d)
3
3
x  20
9x

x  2 dx
3
 2 x )( x  7 ) dx
f ) (x
2
4
dx
 2 x )e
5
2
x  5 x  12
2. a) A marginal average profit function is
dx
MAP   0 . 15 
3000
x
The average profit per unit if 100 units are produced is $55. Find the profit function.
b) Find
dy
y ( t ) if
dt
dy
c) Find y(t) if
t

t
2
 4 te
t
1
2
and y ( 0 )  6
.
and y ( 0 )   3
dt
3. Find the left and right hand Riemann sums using 5 equal subintervals of [ 1, 3] for
f (x) 
1
.
x
b
4. Show that
xe
x
e
x
is an antiderivative for
xe
x
and evaluate
 xe
x
dx
.
a
5. Evaluate each.
4
a)

f ( x ) dx
1

2
1 x
f (x)  
 x  1
1  x  1
1 x
4
b)
t
t
2
 1 dt
4
c)
x 2 
 e t dt 
dx 

0

d

x
d)
d  t2 
 dt

 dt  e
0
6. a) Find the area between the graphs of f ( x )  2 x 2  7 x  12 and g ( x )  x 2  6 x
for x between -5 and 5.
b) Find the area between the graphs of f ( x )  2 x 2  7 x  12 and g ( x )  x 2  6 x .
7. Find the consumer surplus and producer surplus at equilibrium for
demand and supply prices
a) D ( x )  46  0 . 02 x 2 S ( x )  10  0 . 02 x 2
b)
D ( x )  46  0 . 01 x
2
S ( x )  10  0 . 03 x
2