Volume
Cylindrical Shells
2(radius)
(height)
F=ma
Method of Disks
Area = (outer radius)2 (inner radius)2
Volume is integral of area.
Get cross
section
of area,
find area of that
Usually if around revolve
around
horizontal
line,
and
integrate
it
from
a
to
Math 162: Calculus IIA
First Midterm Exam ANSWERS
October 11, 2013
1. (20 points)
A swimming pool is 20 feet wide, 50 feet long and 5 feet deep. It is partly lled with water
to a depth of 4 feet. How much work is needed to pump all the water out of the po
MIDTERM 1 REVIEW SHEET
1. THE SUBSTITUTION RULE
If u = g (x) is a dierentiable function and f is continuous on the range of g , then
f (g (x)g (x) dx =
f (u) du
In the case of denite integrals, if g (x) is continuous on [a, b] and f is continuous on the
r
Math 162: Calculus IIA
Second Midterm Exam ANSWERS
November 14, 2013
1. (20 points) Consider the curve
x4
1
+ 2.
16 2x
f (x) =
(a) Calculate the arc length function s(t) starting at x = 1, that computes the length of the
curve from (1, f (1) to (t, f (t).
Math 162: Calculus IIA
Second Midterm Exam ANSWERS
November 10, 2011
1. (20 points)
(a) Compute the area of surface of revolution obtained by rotating the curve y = x3 , for
0 x 1, about the x-axis.
(b) Do the same for the curve y = |x|, for 1 x 1.
Soluti
Math 162: Calculus IIA
Second Midterm Exam ANSWERS
November 9, 2011
1. (20 points)
(a) Compute the area of surface of revolution obtained by rotating the curve y =
around the x-axis.
(b) Do the same for the curve y = 1 |x|, 1 x 1.
Solution:
(a)
2
A = 2
y
Daniel Wong
MTH 162 Fall 2009
WeBWorK assignment number 12 is due : 12/02/2016 at 06:00am EST.
The home page for the course contains the syllabus, grading policy, and other information.
Alternating series. Ratio and root tests. Absolute Convergence and re
Daniel Wong
MTH 162 Fall 2009
WeBWorK assignment number 14 is due : 12/09/2016 at 06:00am EST.
The home page for the course contains the syllabus, grading policy, and other information.
Representation of functions as power series, Taylor series, and Macla
Daniel Wong
MTH 162 Fall 2009
WeBWorK assignment number 13 is due : 12/02/2016 at 06:00am EST.
The home page for the course contains the syllabus, grading policy, and other information.
Power Series. Representations of Functions as Power Series.
The prima
Daniel Wong
Assignment 5 due 10/07/2016 at 06:00am EDT
fall16mth162
3. (1 point) Evaluate the indefinite integral.
1. (1 point) For each of the indefinite integrals below, select
which of the following trig substitutions would be most helpful
in evaluatin
Daniel Wong
MTH 162 Spring 2015
WeBWorK assignment number 3 is due : 09/23/2016 at 06:00am EDT.
The home page for the course contains the syllabus, grading policy, and other information.
Volumes and Work.
The primary purpose of WeBWorK is to let you know
Daniel Wong
MTH 162 Fall 2009
WeBWorK assignment number 10 is due : 11/11/2016 at 06:00am EST.
The home page for the course contains the syllabus, grading policy, and other information.
Series and integral test.
The primary purpose of WeBWorK is to let yo
Daniel Wong
Assignment 9 due 11/04/2016 at 06:00am EDT
fall16mth162
1. (1 point)
You are given the polar curve r = 3 cos().
2. (1 point)
Find the length of the spiral r = for 0 4.
Answer :
Solution:
Solution: We use the formula for the arc length. In this
Daniel Wong
Assignment 8 due 10/28/2016 at 06:00am EDT
fall16mth162
(b) Using less than and greater than notation, list the tinterval where the curve is concave upward.
Use upper-case INF for positive infinity and upper-case
NINF for negative infinity. If
Daniel Wong
Assignment 7 due 10/21/2016 at 06:00am EDT
fall16mth162
(correct)
1. (1 point) Find the area of the surface obtained by rotating
the curve
y = 1 + 4x2
Correct Answers:
sqrt(4)*pi/6*[(4*5-8+4)(3/2)-4(3/2)]
4. (1 point)
Which of the following i
Daniel Wong
Assignment 4 due 09/30/2016 at 06:00am EDT
fall16mth162
(d)
Is the following statement true?
1. (1 point) (a) Find the average value of f (x) = 25 x2 on
the interval [0, 4].
Average( f ) Average(g) = Average( f g)
Answer:
A. Yes
B. No
(b) Fi
Daniel Wong
Assignment 6 due 10/14/2016 at 06:00am EDT
fall16mth162
1/[(p-1)2]*[b(1-p)*[(1-p)*ln(b)-1]+a(1-p)*[(p-1)*ln(a)+1
a(1-p)*[(p-1)*ln(a)+1]/[(p-1)2]
1. (1 point) Determine whether the integral is divergent or
convergent. If it is convergent, eva