Calculus
Study Guide for Chapter 4 test
Name _________________________
1. Evaluate the integral:
  4x
2. Evaluate the integral:
  t
3. Evaluate the integral:
 x5  x3 
  x3  dx
3
 3x 2  2 x  1 dx
1
dt
4 

4. Find the particular solution of the equation f ( x)  4 x
f (1)  12 .
1
2
that satisfies the condition
5. Find y  f ( x) if f ( x)  x 3 2 , f (4)  2 , and f (0)  0 .
6. An object has a constant acceleration of 32 feet per second squared, an initial velocity
of -12 feet per second, and an initial position of 4 feet. Find the position function
describing the motion of this object.
1
Ch. 4 study guide
 2i  2 
 
i 1  n  n 
n
7. Find the limit of s(n) as n   . s(n)   
2
 2i   2 
8. Find the limit: lim  1    
n 
n  n
i 1 
n
9. What definite integral represents the area of the shaded region?
8
6
4
2
y = 8 – x2
1 2
10. Write the definite integral for the area of the region bounded by the graphs of
y = 16 – x2 and y = 0.
2
Ch. 4 study guide
11. Choose the correct statement given that
 f ( x)dx  16
0
2
b.
 f ( x)dx  4
0
0
c.
 f ( x)dx  4
2
2
d.
 f ( x)dx  16
0
e. None of these
1
12. Evaluate the integral:
 (1  3x)dx
2

1
13. Evaluate the integral:
4

t  3 dt
0
5 4
14. Evaluate the integral:
  cos x  dx
 4
0
15. Evaluate the integral:
 x  3 dx
5
3
Ch. 4 study guide
8
0
2
 f ( x)dx  10 and  f ( x)dx  6
1
a.
8
16. Find the average value of f ( x)  3x2  2 x on the interval [1, 4].
17. Evaluate the integral:
 x  x 2  13  dx
 

18. Evaluate the integral:
x
19. Evaluate the integral:
  cos8x  dx
2

x3  1 dx
20. Find the area of the region bounded by the graph of y  2 x2  3x  2 , the x-axis, and
the vertical lines x = 0 and x = 2.
4
Ch. 4 study guide
Answers
1. x4  x3  x2  x  C
1
C
3t 3
12. 
3
2
x3
 xC
3
13. 
11
5
2. 
3.
11. b
4. f  x   8 x  4
14.  2
5. f  x   4 x  3x
15.
6. s  t   16t 2  12t  4
16. 16
7. 2
17.
26
8.
3
3
2 3
18.  x  1 2  C
9
9.
10.
 8  x  dx
8
2
0
 16  x  dx
4
2
4
5
Ch. 4 study guide
13
2
4
1 2
x  1  C

8
19.
1
sin 8 x  C
8
20.
10
3