1124worksheet1 - x dx Your signature(5 Use geometry to...

Polytechnic Institute of NYU
MA 1124 Worksheet 1
Print Name:
Signature:
ID #:
Instructor/Section:
Directions: Show all your work for every problem.
Problem Possible Points
1 12
2 12
3 12
4 20
5 12
6 10
7 10
8 12
Total 100

Your signature:
(1) The velocity v ( t ) in the table below is decreasing, 4 ≤ t ≤ 16. Using n=6 subdivi-
sions to approximate the total distance traveled, find
t 4 6 8 10 12 14 16
v ( t ) 104 92 85 78 69 65 54
(a) an upper estimate
(b) an lower estimate

Your signature:
(2) Find the difference between the upper and lower estimates of the distance traveled
at velocity f ( t ) on the interval a ≤ t ≤ b for n subdivisions.
(a) f ( t ) = 4 t + 7, a = 2, b = 6, n = 200
(b) f ( t ) = cos t , a = -
π
4
, b =
π
2
, n = 100

Your signature:
(3) Given the following figure:
(a) Find
Z
2
- 3
f ( x ) dx .
(b) Find
Z
4
- 3
f ( x ) dx .
(c) Find the area of the shaded region.

Your signature:
(4) Use the following figure to find the integrals.
(a)
Z
3 . 5
. 5
f ( x ) dx
(b)
Z
4 . 5
. 5
f ( x ) dx
(c)
Z
4 . 5
2
f ( x ) dx
(d)
Z
. 5
3 . 5
f ( x ) dx
(e)
Z
2