Chapter 3(C) - Application of Integration Area between two...

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Application of Integration
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Area between two curves dx x f x g A b a )) ( ) ( ( - = y = g ( x ) y = f ( x ) x a b A Top curve bottom curve -
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Area between two curves Consider ( ) () g x fx gx y x b a 0 y x b a 0 y x b a 0 y x b a 0 Area between the two curves ( ) ( ) b a g x dx =-
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Area between two curves ( ) ( ) c a A g x fx dx =- () gx y x 0 a c (find) b ( ) ( b c B f x dx A B
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Area between two curves 123 (( ) ( )) ( ( ) ( ) ( cd ac b d AA A g x fx d x f x g x dx g x dx ++ =- +- +- ∫∫ x a b A 1 A 2 A 3 c d () y gx = y fx =
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2 Find the area enclosed by the parabola 2 and the line . y x yx = - =- y 2 2 x 2 2 x y - = x y - = 1 - 0 2 2 Consider 2 20 ( 2) ( 1 )0 or 1 xx -=- --= - += = 2 2 1 2 2 1 2 32 2 1 Are a 2 ( ) 1 2 4 units 3 22 x x dx x x dx x - - - = - -- = -+   
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-2 0 4 2 2 x y x y = 2 - = x y Find the area of the region in the first quadrant bounded by the curves and 2. y x yx = =- 4 0 4 3 2 2 0 2 Are a ( 2) 21 2 32 16 units 3 x x dx x xx = --  = -+   = ( 29 2 Consider 2 20 ( 2) ( 1 )0 2 or 1 (Not possible) 4 xx x -= - -= - += = = take positive root x = Domain : 0 y =≥
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Find the area bounded by the curves , 2 and the -axis. yx y xy = =- Find the area of the region in the first quadrant bounded by the curves and 2. y x = Pause and Think !!! What is the difference between the two questions ???
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This note was uploaded on 11/01/2011 for the course MATH 1505 taught by Professor Yap during the Spring '11 term at National University of Singapore.

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Chapter 3(C) - Application of Integration Area between two...

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