BC 1-2
Quiz #8
Name: ________________
Show all appropriate work clearly for full credit. NO CALCULATORS
Skills
1.
Express the following integral as a limit of Riemann sums. (Do not try to evaluate!)
 
2
3
2.

2 x  3 dx
Evaluate the limit by writing it as an equivalent definite integral, then evaluating the
integral:
n 
2
6k   3  

lim
 7  3      
 
n
n   n  
k 1 

3.
Find the difference between the left- and right- Riemann sums on the interval 1  x  4
for n subdivisions.
f ( x)  e x , n  1000
BC 1-2
4.
Quiz #8
Suppose

4
0
  x  dx  3 ,
(a)
Evaluate
(b)
Evaluate

0
4
(c)
Evaluate


4
1
4
  x  dx  7 , and
2  x  dx .
4
1

4
(   x   3) dx .
 7  x   x  dx .
Name: ________________

1
4
  x  dx  6 .
BC 1-2
5.
Quiz #8
Name: ________________
Evaluate each integral by whatever means you choose. Explain or show work:
a.
b.
c.
d.
e.
2
  sin( x) dx


3
0
x  1 dx
 1 
dx
1  1  x 2 


1


2

2
0
2
4  x 2 dx
sin( x3 ) dx
BC 1-2
Quiz #8
Name: ________________
Concepts:
6.
Evaluate the integral:

4
0
7.
e( x2)  x3  6 x2  12 x  8 dx
2

1
1


For n an integer, evaluate the limit: lim 
n 
 n2  02
n2  12



n2  (n  1)2 
1