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Unformatted text preview: x = (2  1)/5 = 1/5 s So, the Midpoint Rule gives: 2 1 1 dx x âˆ« Example 5 (5.2) [ ] 2 1 1 (1.1) (1.3) (1.5) (1.7) (1.9) 1 1 1 1 1 1 5 1.1 1.3 1.5 1.7 1.9 0.691908 dx x f f f f f x â‰ˆ Î” + + + + = + + + + â‰ˆ âˆ« MIDPOINT RULE As f ( x ) = 1/ x for 1 â‰¤ x â‰¤ 2, the integral represents an area, and the approximation given by the rule is the sum of the areas of the rectangles shown. Example 5 PROPERTIES OF INTEGRALS If it is known that find: 10 8 ( ) 17 and ( ) 12 f x dx f x dx = = âˆ« âˆ« Example 7 (5.2) 10 8 ( ) f x dx âˆ« 8 10 10 8 ( ) ( ) ( ) f x dx f x dx f x dx + = âˆ« âˆ« âˆ« 10 10 8 8 ( ) ( ) ( ) 17 12 5 f x dx f x dx f x dx === âˆ« âˆ« âˆ«...
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This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.
 Fall '08
 Noohi
 Calculus

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