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M408L Final Exam Review – Day 1
- A car is traveling 60 mi/hr when the brakes are fully applied, skidding the car to a stop
at a constant deceleration of
2
22 ft / sec. What is the length of the skid mark on the
highway? (Hint: 60 mi/hr = 88 ft/sec)
A) Write a Riemann sum expression (using
n subintervals) for the area of the
region under the graph of
4
f ( ) x x
on the interval [0,3]
B) Determine the definite integral I to which the Riemann sum
3
1
n
i
i
n n
corresponds.
i)
2 3
0
I (2 x ) dx
ii)
6 3
2
I x dx
iii)
3
4
0
x
I dx
iv)
5 3
1
I (2 x ) dx
A) If
2
2cos( )
( ) ln( )
t
x
F x t e dt
Find
/
F (0)
B) For
3
2
2
x
t
x
G x e dt
Find G '( ) x
- Evaluate the integral
4
0
4sin 6
sin 3
x
I dx
x
- Determine the indefinite integrals
A)
2
3 3
x
dx
x x
B)
3
x
dx
x
C)
3 4 2ln
6
x x
e dx
- Let be the area bound between the functions:
2
( )
x
f x e , y^ ^4 , x 0
A) Write an integral which expresses the volume of the solid formed by rotating
the area about the x-axis.
B) Write an integral which expresses the volume of the solid formed by rotating
the area about the y-axis. What technique is necessary to evaluate such an
integral?
- Determine the indefinite integrals
A)
2
2
x x
dx
x x
B)
2
x
dx
x
C)
dx
x x
- Determine the limits
A)
6 0
lim
x
x
e
x x
B)
0
3 ln
lim
x
x x
x
C) (^)
5
0
lim cos3 x
x
x
D)
1
lim
ln 1
x x x
- Determine the integrals
A) x^ cos(5 ) x dx
B)
3
x ln( ) x dx
C)
2
sin(3 )
x
x e dx
D) sin^ xdx
- Determine the integrals
A)
2
tan x dx
B)
3
4
sin
cos
x
dx
x
C)
2 2 3
(cos x sin x ) dx
- Determine the indefinite integral
A)
5
5
2 2
2
1
25
dx
x x
B)
2 2 3/ 2
1
(( ) )
dx
ax b
C)
0
2 2 1 ( 2 2)
dx
x x
D)
3
2
2
2 5/ 2 2 (5 4 )
dx
x x
