BC Calculus
Chapter 6 Practice Exam
1.
Given the function f ( x)  e x  x3 on the interval [1, 3.5], estimate the area
bounded by f and the x-axis using MRAM5.
2.
Use your calculator to evaluate
3.
Evaluate by hand

4.
5.

3
3
sec2 x dx 

b
a2
5 x dx where b > a.
9
4.1
  6x  4 dx.
8
6
Evaluate

ln x
dx.
x  cos x
6.
7.
Given the function y  0.3x  1.5x on the interval 0  x  6.
a)
Sketch the function on the axes below
b)
Integrate y over the interval [0, 6].
c)
Find the area of the region between the graph of y and the x-axis.
Let f ( x)  3x  2 .
a)
Find the value of K so that
b)
Find
d x2
f (t ) dt .
dx 1

x
2
x
f (t ) dt  K   f (t ) dt.
8
8.
Use Trapezoidal sums with 4 trapezoids of equal width to approximate the value
of
9.
  4  x  dx .
5
2
1
Suppose that g and h are continuous functions that that

6
2
g ( x) dx  5,

6
2
h( x) dx  1, and

6
5
h( x) dx  3.
Which of the following must be true?
I.

6
II.

6

5
III.
10.
2
5
2
g ( x)
dx  5.
h( x )
4h( x) dx  12.
h( x) dx  4.
A particle moves along the x-axis. Its position (in centimeters) at any time t
t
(seconds) is given by s(t )   f ( x) dx where f is the function shown below.
0
a)
What is the position of the particle are t = 0?
b)
What is the position of the particle at t = 3?
c)
What is the velocity of the particle at t = 5?
d)
Approximate when will the acceleration of the particle equal zero?
e)
At time (approximately) during the first 7 seconds does s have its largest
value?
11.
What is the average value of y  tan x
  
on  ,  ?
6 3