BASIC COMPONENTS OF
SOCIAL STRATIFICATION
SOCIAL CLASS
Class
is large group of people regarded by
themselves or others as sharing similar status
with regard to wealth, power and prestige.
SOCIAL STATUS
Standing
of a person within a social class or in
th
INTEGRATION OF
INVERSE TRIGONOMETRIC
FUNCTIONS
Review
Recall derivatives of inverse trig functions
d
1 du
1
sin u =
, u <1
dx
1 u 2 dx
d
1 du
1
tan u =
dx
1 + u 2 dx
d
1
du
1
sec u =
, u <1
dx
u u 2 1 dx
2
Integrals Using Same Relationships
du
u
a 2 u 2
TOPIC
Integration of
Hyperbolic Functions
OBJECTIVES
OBJECTIVES
identify the different hyperbolic functions;
find the integral of given hyperbolic functions;
determine the difference between the integrals
of hyperbolic functions; and
evaluate integrals in
INTEGRATION OF
INVERSE HYPERBOLIC
FUNCTIONS
Review
Theorem 6.9.4 (p. 480)
Review
Theorem 6.9.5 (p. 481)
Review
Theorem 6.9.6 (p. 481)
Comparison of Integrals
(Inverse Trig & Inverse Hyperbolic)
1.
du
a u
2
2
= sin
1
u
+C
a
du
1
u
2. 2
= tan 1 + C
a
a + u2
TOPIC
TECHNIQUES OF INTEGRATION
TECHNIQUES OF INTEGRATION
1. Integration by parts
2. Integration by trigonometric substitution
3. Integration by miscellaneous substitution
4. Integration by partial fraction
TECHNIQUES OF INTEGRATION
1. Integration by part
TOPIC
TECHNIQUES OF INTEGRATION
TECHNIQUES OF INTEGRATION
1. Integration by parts
2. Integration by trigonometric substitution
3. Integration by miscellaneous substitution
4. Integration by partial fraction
TECHNIQUES OF INTEGRATION
2. Integration by trig
TOPIC
TECHNIQUES OF INTEGRATION
TECHNIQUES OF INTEGRATION
1. Integration by parts
2. Integration by trigonometric substitution
3. Integration by miscellaneous substitution
4. Integration by partial fraction
TECHNIQUES OF INTEGRATION
3. Integration by misc
TOPIC
TECHNIQUES OF INTEGRATION
TECHNIQUES OF INTEGRATION
1. Integration by parts
2. Integration by trigonometric substitution
3. Integration by miscellaneous substitution
4. Integration by partial fraction
TECHNIQUES OF INTEGRATION
4. Integration by part
TOPIC
LENGTH OF AN ARC
OBJECTIVE
discuss the formula for computing length of an arc;
compute the length of an arc.
Lengths of curves
To find the length of the arc of the curve y = f (x) between x = a and
x = b let s be the length of a small element of arc
TOPIC
APPLICATIONS
AREA BY INTEGRATION
The area under a curve
Let us first consider
the irregular shape
shown opposite.
How can we find the
area A of this shape?
The area under a curve
We can find an
approximation by
placing a grid of
squares over it.
By
TOPIC
APPLICATIONS
VOLUME BY INTEGRATION
OBJECTIVE
define what a solid of revolution is
decide which method will best determine the
volume of the solid
apply the different integration formulas.
DEFINITION
A solid of revolution is the figure formed when a
TOPIC
APPLICATIONS
CENTROIDS OF PLANE AREA
DISCUSSION
The mass of a physical body is a measure of the quantity of the matter in it,
whereas the volume of the body is a measure of the space it occupies.
If the mass per unit volume is the same throughout th
TOPIC
APPLICATIONS
CENTROIDS OF SOLIDS OF
REVOLUTION
Center of gravity of a solid of revolution
The coordinates of the centre of gravity of a solid of revolution are
obtained by taking the moment of an elementary disc about the
coordinate axis and then su
Wo do b a s
rk ne y pring
Wo do b pum aliq
rk ne y
ping uid
Work done by a spring
Hookes Law
Ho ke Law s sthat within the
o s
tate
lim o e tic thedis e e pro e in a
its f las ity
plac mnt duc d
b dy ispro rtio to
o
po nal
thefo eapplie that is, F =kx, w
WALLIS FORMULA
TRIGONOMETRIC TRANSFORMATION
WALLIS FORMULA
OBJECTIVES:
recall and apply the different trigonometric
identities in transforming powers of sine and
cosine; and
use Wallis Formula to shorten the solution in
finding the antiderivative of power
ANTIDERIVATIVES
(INTEGRAL)
TRANSFORMATION OF
TRIGONOMETRIC FUNCTIONS
OBJECTIVES:
integrate functions of the nth power of the
different trigonometric functions; and
correlate the basic trigonometric integration
formulas in evaluating the integral of the nt
ANTIDERIVATIVES
(INTEGRAL)
THE BASIC TRIGONOMETRIC
INTEGRATION FORMULAS
OBJECTIVES:
recall and apply the different trigonometric
identities in simplifying a function; and
integrate trigonometric functions using their
differentials as the basis for evaluat
School of Languages, Humanities and Social Sciences
Mapa Institute of Technology
Written Task # 1:
An FBI Paper on Allowing Transgender in Miss Universe
Presented by:
Kimberly Mae D. Somis
SS11 B3
Presented to:
Prof. Gil Astrophel B. Orcena
Date of Submis
There have been various cases of unequal treatment in the Philippine society and some of these are the
discrimination, rejection, exploitation and abuse against the LGBT community. One example of this is when the
Comelec rejected Ang Ladlad for party-list
1:00-1:05 - Opening prayer (MARK)
1:05-1:10 - Opening remarks (if possible, someone from the barangay)
1:10-1:25 - Introduction of the group, purpose and importance of the activity (DAREN)
1:25-1:50 - Getting to know, icebreaker, explain the coming sessio
Good afternoon Prof. Orcena, Good afternoon classmates. Im James Samia and I was assigned
to discuss the basic components of social stratification.
First slide:
Social stratification has three basic components. For the first basic component, the social cl
School of Languages, Humanities and Social Sciences
Mapa Institute of Technology
Written Task # 1:
An FBI Paper on RH Bill
Presented by:
James Elicio H. Samia
SS11 B3
Presented to:
Prof. Gil Astrophel B. Orcena
Date of Submission:
26 April 2012
I.Backgrou
GENERAL SOCIOLOGY
Prof. Gil Astrophel B. Orcena, MA Sociology
COURSE INTRODUCTION
1. Introduce and develop liberal perspectives in the course.
2. Contribute something new to a field of inquiry
3. A systematic way to determine ones contribution to inquiry
There have been numerous cases of discrimination in our culture and one of these is the
discrimination against the LGBT community. In Don Bosco Pampanga, an all boys school from
where I came from, those who are confirmed gays are expelled and must transfe
Summary (SAM)
The impeachment trial of Chief Justice Renato Corona began on January 16, 2012 after
the Lower House of Congress passed the articles of impeachment to the senate and approved last
December 13, 2011. Betrayal of public trust by being a midnig
ANTIDERIVATIVES
(INTEGRAL)
THE INDEFINITE INTEGRAL AND THE
BASIC INTEGRATION FORMULAS
OBJECTIVES:
know the relationship between differentiation
and integration;
identify and explain the different parts of the
integral operation; and
perform basic integrat
GENERALIZED POWER
FORMULA
(Integration by Simple
Substitution)
MATH22
INTEGRAL CALCULUS
GENERALIZED POWER
FORMULA
(Integration by Simple
Substitution)
BJECTIVES:
identify an integrand that can be integrated using
simple substitution;
perform integration
DEFINITE INTEGRAL
MATH 22
INTEGRAL CALCULUS
THE DEFINITE INTEGRAL
BJECTIVES:
define and interpret definite integral,
identify and distinguish the different properties of
the definite integrals; and
evaluate definite integrals
THE DEFINITE INTEGRAL
If F(x)
INTEGRALS YIELDING
THE NATURAL
LOGARITHMIC
FUNCTION
INTEGRALS YIELDING THE NATURAL
LOGARITHMIC FUNCTION
BJECTIVES:
Define the natural logarithmic function;
Illustrate solutions on problem yielding to
natural
logarithmic function;
Derive particular formu
INTEGRATION OF
EXPONENTIAL
FUNCTION
INTEGRATION OF EXPONENTIAL FUNCTION
BJECTIVES:
Define exponential functions;
Illustrate an exponential function;
Differentiate exponential function from other
transcendental function function ;
provide correct solut