sec53 - Section 5.3 Finding the Total Area y y y = f(x y =...

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Section 5.3: Finding the Total Area Shaded Area = b a dx x f ) ( a b y = f ( x ) x y y = g ( x ) a b y x b a dx x g ) ( Shaded Area =

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y= f ( x ) a b y = g ( x ) A) Area Between Two Curves in [ a , b ] y= f ( x ) a b y = g ( x ) Area under f ( x ) = dx x f b a ) ( Area under g ( x ) = dx x g b a ) ( Area between f ( x ) and g ( x ) - = b a dx x g x f )] ( ) ( [ - = b a dx ction Bottom Fun on Top Functi a , b ] [ ] [ in Curves Two Between Area y = g ( x ) y= f ( x ) a b
B) Area Between a Curve and the x -Axis in [ a , b ] x -Axis is same as y = 0 y = 0 y = 0 y = g ( x ) a b y x y = f ( x ) y x b a Area under f ( x ) in [ a , b ] : Top Function is y = f ( x ) Bottom Function is y = 0 - = b a dx Bottom Top ] [ = - = b a b a dx x f dx x f ) ( )] 0 ( ) ( [ Area under g ( x ) in [ a , b ] : Bottom Function is y = g ( x ) Top Function is y = 0 - = b a dx Bottom Top ] [ - = - = b a b a dx x g dx x g ) ( )] ( ) 0 [(

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y = 2 x - 1 1) Graph both functions 2) Find the points of intersection by equating
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This note was uploaded on 02/29/2012 for the course MATH 119 taught by Professor Maanomran during the Fall '09 term at Indiana University-Purdue University Fort Wayne.

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sec53 - Section 5.3 Finding the Total Area y y y = f(x y =...

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