Introduction to Integration
How To Find The Area under a curve - Sigma Notation.
Sigma Notation allows us to express a sum of terms in a very concise way, in its general form it is written
n
as
f (i )
each part of the notation has a specific meaning.
i 1
Section 6.3 - Volumes By Cylindrical Shells.
The volume of a solid obtained by rotating
the curve y = f(x) about the y-axis from
x = a to x = b is
The volume of a solid obtained by rotating
the curve x = f(y) about the x-axis from
y = c to y = d is
d
b
V
Section 6.2 - Volumes Of Revolution Disks
b
The volume of a solid from x = a to x = b can be found by using the formula. V =
A( x)dx
a
Where A(x) is the vertical cross sectional area at the general point x.
y
y = f(x)
y
0
a
b
x
This is a typical disk at
Scientific Notebook Introduction
Scientific Notebook is a very versatile program as it allows you to write mathematical text as in a word
processor but it also allows you to manipulate and calculate many mathematical processes. Scientific
Notebook is simi
Introduction To Integration(Reimann Suims)
Example 1:
Estimate the area under the curve from x = 0 to x = 12 by calculating L6 and R6 and M6
Solution:
We estimate the area under the curve by calculation L6 , called the Left estimate, this is done by
using
Chapter 5.3 - The Fundamental Theorem of Calculus
Part 2:
If f(x) is a continuous function on the interval [a,b] then the area under the curve from
x = a to x = b can be found by using the result that
()
= F(b) F(a)
where F(x) is the anti-derivative of f(
Math 152 Test 1 Winter 2014
Math 152- Test 1
Students Name_
1.
Evaluate the following definite integrals, you must do so algebraically (cannot use a decimal
estimate from the calculator) and show the relevant working.
2
(a) 1
2x 8x
3
dx
xx
=
2
2x
4
x2
x
Olympic College Topic 2 Solving Equations
Topic 2 Solving Equations
Introduction:
When you are given the value of a variable and an algebraic expression then you can evaluate the
expression.
For example, If you are told that x = 6 then the value of the ex
Olympic College Topic 1 Algebraic Expressions
Algebraic Expressions
1. Introduction:
Definition: In algebra, we use letters such as x, y and z to represent unknown numbers.
For example 5x + 4y an algebraic expression. In this expression we call x the vari
Calculus 152 Project 1- Winter 2014
Math 152 Project I (50 points)
Due Wednesday 15th January
Section I- Multiple Choice
Students Name:_
1.
A.
C.
2.
x
What is the derivative of the function y =
1
2x
1
2x
1
2 x3
1
B.
22
1
2x
D.
3
1
x
2
1
2x
1
2x
The positi
Solutions to Work Questions.
13.
A heavy rope 50ft long, weighs 0.5 pounds per foot and hangs over the edge of a building
120 ft high.
(a)
How much work is done in pulling the rope to the top of the building?
The total height of the building (200ft ) is n
Function f(x)
Antiderivative F(x)
f(x) = axn
f(x) =
F(x) =
1
x
a n 1
x +C
n 1
F(x) = ln(x) + C
f(x) = sin x
F(x) = cos x + C
f(x) = cos x
F(x) = sin x + C
f(x) = sec2 x
F(x) = tan x + C
f(x) = sec x tan x
F(x) = sec x + C
f(x) = csc x cot x
F(x) = csc x +