Volumes
Section 6.2
Lecture 7 Objectives
Evaluate volumes of spatial regions by choosing an
appropriate axis, and slicing the region with planes
that are perpendicular to that axis.
Evaluate volumes resulting from revolving a region
in the xy-plane around
MACT 132: Calculus II
Moataz El-Zekey
Course Material
Calculus, 6th edition, by J. Stewart, Brooks/Cole,
2009
+ Supplementary Material on the Blackboard.
Prerequisites:
Formally: MACT 131 or Exemption
Informally: Chapters 1-4 from the text.
However, apart
Lecture 10
Inverse Functions
Section 7.1
Lecture 10 Objectives
Decide if a function is one-to-one
(injective) using:
The definition
The Horizontal Line Test
Explain the necessity of the function being
one-to-one for having an inverse.
Find the domain, the
Lecture 9
Average Value of a Function
Section 6.5
Lecture 9 Objectives
Find the average value of a function on a
given interval.
Apply the Mean Value Theorem for
Integrals.
The Average Value
Recall:
For a finite sequence of numbers y1 , y2 , ,
yn , the av
The Definite Integral
Section 5.2
Lecture 2 Objectives
Define the definite integral of a continuous
function, and interpret it in terms of areas above
and below the x-axis.
Evaluate the definite integral of simple functions:
Using the definition and the s
Areas between Curves
Section 6.1
Lecture 6 Objectives
Evaluate areas of regions bounded between two (or
more) curves using definite integration with
respect to x (or y).
Estimate areas of regions bounded between two
(or more) curves using Riemann sums and
The Substitution Rule
Section 5.5
Lecture 5 Objectives
Use appropriate substitutions to evaluate
indefinite and definite integrals.
Use (even or odd) symmetry of functions to
evaluate their integrals on symmetric intervals.
A Motivating Example
cos( x
2
The Fundamental Theorem of Calculus
Section 5.3
Lecture 3 Objectives
Apply Part 1 of the Fundamental Theorem of
Calculus, properties of the definite integral, and
the chain rule, to find the derivatives of functions
defined using definite integrals.
Apply
MACT 1122
Review Session for Midterm 1
Fall 2014
1
sin(x4 ) dx. Is
1) Use left-endpoints and 4 subintervals to estimate the integral
0
2)
3)
4)
5)
your approximation an upper-estimate, lower-estimate, or neither?
[( )
]
( )9 ( )9
9
( n )9
1
1
2
3
Evaluate
MACT 1122
Spring 2015
Midterm 1
March 3, 2015
Name:
UID:
Section Number:
Show your work to receive full credit.
Only scientic calculators are allowed.
Time: 75 minutes.
Problem Score Points
1
31
2
24
3
18
4
21
5
16
Total
110
MACT 1122
Spring 2015
Probl
MACT 132
Spring 2013
Midterm 1
March 2, 2013
UID:
Name:
Circle your section:
1
2
3
4
5
6
Show your work to receive full credit.
Calculators are allowed.
Time: 75 minutes.
Problem Score Points
1
15
2
28
3
16
4
16
5
14
6
16
Total
105
7
8
MACT 132
Spring
MACT 1122
Review Sheet for Midterm 1
Summer 2015
1) Answer the Concept Check problems on p. 337.
2) Do the True-False Quiz on p. 338.
3) Do the following exercises starting p. 338-340:
1, 3, 4, 5, 7, 8, 11, 13, 15, 17, 19, 21, 23, 27, 35, 37, 43, 45, 48,