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