5.3 The Definite Integral

5.3 The Definite Integral - 1 5.3 The Definite Integral We...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 5.3 The Definite Integral We have approximated the area under the graph of a function by using rect- angles. The thinner the rectangles the better the approximation. Exact area under the graph can be defined as a limit of the approximations , where x is the ( ) of each rectangle and f ( x i ) is the of the i th rectangle. This motivates the following defintion: Definition If f is a function on the interval [ a,b ], we divide the [ a,b ] into n subintervals of equal width x = . The of f from a to b is: = where x k is point inside k th subinterval. REMARKS: The definite integral is a It represents the area under the graph only if on [ a,b ] If f ( x ) < 0 somewhere inside the interval, the definite integral represent the area under the graph. If f ( x ) < 0 somewhere on [ a,b ] the definite integral represents the sum of the area under the graph where MINUS the area between the axis and the graph where ....
View Full Document

This note was uploaded on 10/02/2011 for the course MATH 1206 taught by Professor Llhanks during the Fall '08 term at Virginia Tech.

Page1 / 5

5.3 The Definite Integral - 1 5.3 The Definite Integral We...

This preview shows document pages 1 - 2. Sign up to view the full document.

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