Integral Calculus & Ord. Diff. Equations 2016 ,AIUB
Chapter 2
Applications of the Definite Integral
2.1 Area of regions between two curves
Definite integrals could be used to determine the area of the region between the graph of a
function and the x-axis
Integral Calculus & Ordinary Differential Equations
Summer 2015-2016, AIUB
Chapter 3
Methods of Integration
3.1 Integration by Parts
Suppose that u and v are differentiable. From the product rule
.
d
dx
uv u dv
v du
dx
dx
x and transposing, we have
.
In
Integral Calculus & Ordinary Differential Equations
Summer 2015-2016, AIUB
Chapter 4
Improper Integrals, Gamma and Beta Functions
4.1 Improper Integrals
An improper integral is an extended concept of a definite integral that has infinite limits on
one or
Chapter 9 (Continue)
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AMERICAN INTERNATIONAL UNIVERSITY-BANGLADESH
Faculty of Science and Information Technology
Department of Mathematics
COURSE OUTLINE
Academic Term: Summer 2014-2015
I-
Course Code and Title : MAT1205, Integral Calculus
and
Equations
Ordinary Differential
I
Chapter 3
Techniques of Integration
3.1 Integration of Rational Functions
A function of the form P(x)/Q(x), where P and Q are polynomials are rational function. It is
said to be proper fraction if the degree of P(x) is less than degree of Q(x), otherwise,
Chapter 1
Indefinite Integration
1.1 Indefinite Integrals
Indefinite integration may be regarded as the inverse operation to differentiation. This means
that the derivative of an indefinite integral of a function is the function itself.
Definition: Suppos
Chapter 2
Definite Integration
2.1 Definition of a Definite Integral
Let
f (x)
be defined (i.e. bounded) in the interval
I [a, b]
. Sub Divide I into n subintervals by
the points
a x 0 x1 x 2 x n b
and let
x r x r 1 x r
For each r choose a point
cr
,
such