MTH 201
Chapter 6: Application of Integration
Spring 2017
6.6 Work Worksheet
1. A crane has a cable used to lift and move various objects. The cable is 300 long and weighs a total of
2000.
(a) If half of the cable is currently out and needs to be retracte
Math 201 Calculus II
Suggested Problems for Chapter 6
The following problems are suggested problems for chapter 6. I
will not collect these for a grade.
Section
6.1
Problems
1 18 and 27 38
6.2
1 - 48
6.3
1 - 32
6.4
1 14 and 27 - 32
6.5
1 22 and 25 30
6.6
MTH 201
Chapter 6: Application of Integration
Spring 2017
6.2&6.3 Volumes Worksheet
1. Let be the finite region bounded by the graphs of = ln() , = 3, = 5, & = 0. Set up a definite
integral which represents the volumes of the following solids. Use your ca
MTH 201
Chapter 6: Application of Integration
Spring 2017
6.2&6.3 Volumes Worksheet
1. Let be the finite region bounded by the graphs of = ln() , = 3, = 5, & = 0. Set up a definite
integral which represents the volumes of the following solids. Use your ca
MTH 201
Chapter 6: Application of Integration
Spring 2017
6.1 Areas Between Curves Worksheet
1. Find the area of the region enclosed by the curves = 2 and = 2 2 .
Find Intersections:
2 = 2 2
Setup:
2 2 2 = 0
2( 1) = 0
= 1 = 0
(1,1)
1
= [(2 2 ) 2 ]
0
E
MTH 201
Chapter 6: Application of Integration
Spring 2017
6.1 Areas Between Curves Worksheet
1. Find the area of the region enclosed by the curves = 2 and = 2 2 .
2. Let be the finite region bounded by the curves = 5 tan() , = 5, and = 0. Set up, but do n
MTH 201
Chapter 6: Application of Integration
Spring 2017
6.4 Arc Length Worksheet
1. Find the exact arc length of the curve over the given interval: y x 2 from x 1 to x 3 .
(a) Set up, but do not evaluate, an integral with respect to x.
(b) Set up, but d
MTH 201
Chapter 6: Application of Integration
Spring 2017
6.5 Surface Area Worksheet
1. Find the surface area of the solid generated by revolving the curve y x , 1 x 4 about the x-axis.
Set up integrals with respect to x and y and then evaluate one of the
MTH 201
Chapter 6: Application of Integration
Spring 2017
6.6 Work Worksheet
1. A crane has a cable used to lift and move various objects. The cable is 300 long and weighs a total of
2000.
(a) If half of the cable is currently out and needs to be retracte
MTH 201
Chapter 6: Application of Integration
Spring 2017
6.4 Arc Length Worksheet
1. Find the exact arc length of the curve over the given interval: y x 2 from x 1 to x 3 .
(a) Set up, but do not evaluate, an integral with respect to x.
We note that y 2
MTH 201
Chapter 6: Application of Integration
Spring 2017
6.5 Surface Area Worksheet
1. Find the surface area of the solid generated by revolving the curve y x , 1 x 4 about the x-axis.
Set up integrals with respect to x and y and then evaluate one of the