Lecture 8 - CC2053 Calculus 8 Introduction to Calculus and...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
1 CC2053: Calculus 8 Introduction to Calculus and Linear Algebra 2011/2012 Semester 1 INTEGRATION: Definite Integrals
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 CC2053: Calculus 8 Definition of a Definite Integral Let f be a continuous defined on the closed interval a x b , and let 1. a = x 0 < x 1 < ····· < x n-1 < x n = b 2. Δ x k = x k x k -1 , for k = 1, 2, ··· , n 3. Δ x k 0 as n →∞ 4. for k = 1, 2, ··· , n
Background image of page 2
3 CC2053: Calculus 8 Definition of a Definite Integral Then is called definite integral of f from a to b. The integrand is f (x), the lower limit is a , and the upper limit is b.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 CC2053: Calculus 8 Area Under a Curve
Background image of page 4
5 CC2053: Calculus 8 Area Under a Curve If f ( x ) is continuous f ( x ) 0 on the interval a x b , then the region under the curve y = f ( x ) above a x b has area
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
6 CC2053: Calculus 8 Fundamental Theorem of Calculus If f ( x ) is continuous function on the closed interval a x b and F ( x ) is any antiderivative of f ( x ) then
Background image of page 6
7 CC2053: Calculus 8 Example 9 Evaluate a. b. c.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
8 CC2053: Calculus 8 Example 9:- solution a. Let b. Then
Background image of page 8
9 CC2053: Calculus 8 Example 9:- solution c.
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
10 CC2053: Calculus 8 Area between a Curve and the x -axis For a function f continuous over [ a , b ], the area between y = f ( x ) and the x axis from x = a to x = b can be found using definite integrals as follows: For over [ a , b ] For over [ a , b ]
Background image of page 10
11 CC2053: Calculus 8 Example 10 Find the area bounded by and for .
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
12 CC2053: Calculus 8 Example 10:- solution Area -2 2 y = x 2 -4 x y
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 36

Lecture 8 - CC2053 Calculus 8 Introduction to Calculus and...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online