Math 1540 Quiz 4 Practice Fall 2007
Name: Last ____________________. First ____________________
You must show your work and/or provide explanations for your answers for all questions.
Otherwise, no credit will be given.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use a finite approximation to estimate the area under the graph of the given function on the stated interval as instructed.
1)
f(x) = x
2
between x = 0 and x = 3 using an upper sum with two rectangles of equal width.
A)
3.375
B)
16.875
C)
12.5
D)
8.4375
1)
Write the sum without sigma notation and evaluate it.
2)
4
k = 1
2 sin π
k
∑
A)
2 sin π + 2 sin
π
2 + 2 sin
π
3 + 2 sin
π
4 = 6 + 2
B)
2 sin π + 2 sin
π
2 + 2 sin
π
3 + 2 sin
π
4 = 2 + 3 + 2
C)
2 sin π + 2 sin π
2 + 2 sin π
3 + 2 sin π
4 = 1 + 3 + 2
2
D)
2 sin π + 2 sin
π
4 = 2
2)
Solve the problem.
3)
Suppose that g is continuous and that
6
2
g(x) dx = 12
∫ and
9
2
g(x) dx = 16.
∫ Find
6
9
g(x) dx
∫.
A)
-
4
B)
28
C)
-
28
D)
4
3)
Evaluate the integral.
4)
4
0
2 x
∫dx
A)
16
B)
4
C)
24
D)
32
3
4)
5)
2
1
t + 1
t
2
∫dx
A)
15
2
B)
29
6
C)
37
6
D)
5
6
5)
1
