ch6sc1notes

# ch6sc1notes - 1 Math 104 – Rimmer 6.1 Area between curves...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 Math 104 – Rimmer 6.1 Area between curves 6.1 Area Between Curves ( ) ( ) Consider the region that lies between two curves and and between the vertical lines and . S y f x y g x x a x b = = = = ( ) ( ) [ ] Here, and are continuous functions and for all in , . f g f x g x x a b ≥ Math 104 – Rimmer 6.1 Area between curves ( ) ( ) We divide into strips of equal width and approximate the th strip by a rectangle with base and height * * i i S n i x f x g x Δ- 2 Math 104 – Rimmer 6.1 Area between curves [ ] 1 lim ( *) ( *) n i i n i A f x g x x →∞ = =- Δ ∑ [ ] 1 The Riemann sum is therefore an approximation to what we intuitively think of as the area of ( . *) ( *) n i i i f x g x x S =- Δ ∑ This approximation appears to become better and better as . n → ∞ Thus,we define the area of the region as the limiting value of the sum of the areas of these approximating rectangles. A S Math 104 – Rimmer 6.1 Area between curves ( ) ( ) b a A f x g x dx =- ∫ Thus,we have the following formula for area :...
View Full Document

## This note was uploaded on 11/04/2009 for the course MUSIC 021 taught by Professor Gray during the Spring '09 term at UPenn.

### Page1 / 5

ch6sc1notes - 1 Math 104 – Rimmer 6.1 Area between curves...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}