FACULTY MEMBER -MtM MAT-130,
POLAR COORDINATES
Polar Coordinates
So far, weve dealt exclusively with the Cartesian (or Rectangular, or x-y) coordinate
system. However, as we will see, this is not always the easiest coordinate system to
work in. So, in thi
FACULTY ME
MBER -MtM
MAT-130
TRIGONOMETRIC INTEGRALS
Integrals Involving Trig Functions
In this section we are going to look at quite a few integrals involving trig functions and
some of the techniques we can use to help us evaluate them. Lets start off w
FACULTY MEMBER -MtM
MAT-130
TRIGONOMETRIC SUBSTITUTIONS
Trigonometric Substitutions
As we have done in the last couple of sections, lets start off with a couple of integrals
that we should already be able to do with a standard substitution.
Both of these
FACULTY-MtM
MAT-130
VOLUMES BY CYLINDRICAL SHELLS
Volumes of Solids of Revolution/method of shells/Method of Cylinders
In the previous section we started looking at finding volumes of solids of revolution.
In that section we took cross sections that were
FACULTY MEMBER-MtM
MAT-130 AREA OF SURFACE OF REVOLUTION
Surface Area
In this section, we want to find the surface area of the solids of revolution.
So, for the purposes of the derivation of the formula, lets look at rotating the
y f (x )
a, b about the
FACULTY-MtM
MAT-130 VOLUMES BY SLICING DISKS AND WASHERS
Volumes of Solids of Revolution/ method of disks / Method of
Rings (Washers)
In this section we will start looking at the volume of a solid of revolution.
mustak
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9/24/2017
FACULTY-MtM
MAT-130
FACULTY MEMBER-MtM
MAT-130 AREA BETWEEN TWO CURVES
Area under a curve with x-axis
Today, we will find areas under curves (i.e., between the
curve and the x-axis). We will sum up the areas of
rectangles which approximate the area under the curve. We
will u
FACULTY MEMBER -MtM
MAT-130,
IMPROPER INTEGRALS
Improper Integrals
Suppose f(x) is a continuous function on [a,b] and also suppose that F(x) is any antiderivative for f(x). Then,
In this section we will take a look at a couple of different kinds of integr
FACULTY MEMBER-MtM
MAT-130
LENGTH OF PLANE CURVES
Arc Length
In this section we are going to look at computing the arc length of a function.
Because its easy enough to derive the formulas that well use in this section we will
derive one of them and leave
FACULTY MEMBER -MtM
MAT-130,
CONIC SECTIONS IN CALCULUS
Definition: A circle is the set of points in a plane at a
fixed distance from a given point.
To develop the equation for a circle:
Call the given point (h, k) this is the center.
Let the fixed distan
FACULTY MEMBER -MtM
MAT-130,
AREA IN POLAR COORDINATES
Area with Polar Coordinates
In this section we are going to look at areas enclosed by polar curves. Note as well that
we said enclosed by instead of under as we typically have in these problems. These
FACULTY MEMBER -MtM
MAT-130,
TANGENT LINES AND ARC LENGTH FOR PARAMETRIC AND POLAR CURVES
Tangents with Parametric Equations
In this section we want to find the tangent lines to the parametric equations given by,
Here the tangent line to the curve
y F (x
FACULTY MEMBER-MtM MAT-130,
INTEGRATING RATIONAL FUNCTION BY PARTIAL FRACTIONS
Partial Fractions
mustak
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FACULTY MEMBER-MtM MAT-130,
INTEGRATING RATIONAL FUNCTION BY PARTIAL FRACTIONS
There is also another integral that often shows up in t
FACULTY MEMBER-MtM
MAT-130
HYPERBOLIC FUNCTIONS & Integrations
Definition of the Hyperbolic Functions
The set of functions that were going to be looking at are the hyperbolic trig
functions. In many physical situations combinations of
and
arise fairly
oft
FACULTY MEMBER -MtM
MAT-130
INTEGRATION BY PARTS
Integration by Parts
Lets start off this section with a couple of integrals that we should already be able to do to get us started. First lets
take a look at the following.
So, that was simple enough. Now,
Lecture 1 Hyperbolic functions and integrations
Definitions
and graphs of the hyperbolic functions
Sin hyperbolic x = half into e to the power x minus e to the power minus x= half e to the power x + minus half e to the power minus x
Cos hyperbolic x = hal
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Lecture 1,2,3
Contents
Relation
Function
Domain & Range
Absolute Value of Function
Composition of Function
Transformation Method of Plotting Graph
Symmetry
Even & Odd Function
Relation: If x and y are two elements of sets A and B respectively and if a rel
Summer16
NORTH SOUTH UNIVERSITY
DEPARTMENT OF MATHEMATICS AND PHYSICS
ASSIGNMENT
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Section:
Calculus I
s
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Summer16
NORTH SOUTH UNIVERSITY
DEPARTMENT OF MATHEMATICS AND PHYSICS
ASSIGNMENT
Assignment No.: 2
Date of Submission:
Submitted by:
Serial No.:
Course Title:
Student ID:
Course Code:
Full Name:
Section:
Calculus I
s
Department:
Students
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