Pre-Calc Homework Solutions 211

Pre-Calc Homework Solutions 211 - 22. Graph the region...

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Unformatted text preview: 22. Graph the region under y 5 r for 2 w # r # 5 2 w . E 5 2 w 2 w r dr 5 } 1 2 } (5 2 w 2 2 w )( 2 w 1 5 2 w ) 5 24 23. E b x dx 5 } 1 2 } ( b )( b ) 5 } 1 2 } b 2 24. E b 4 x dx 5 } 1 2 } ( b )(4 b ) 5 2 b 2 25. E b a 2 s ds 5 } 1 2 } ( b 2 a )(2 b 1 2 a ) 5 b 2 2 a 2 26. E b a 3 t dt 5 } 1 2 } ( b 2 a )(3 b 1 3 a ) 5 } 3 2 } ( b 2 2 a 2 ) 27. E 2 a a x dx 5 } 1 2 } (2 a 2 a )(2 a 1 a ) 5 } 3 2 a 2 } 28. E 3 w a a x dx 5 } 1 2 } ( 3 w a 2 a )( 3 w a 1 a ) 5 } 1 2 } (3 a 2 2 a 2 ) 5 a 2 29. Observe that the graph of f ( x ) 5 x 3 is symmetric with respect to the origin. Hence the area above and below the x-axis is equal for 2 1 # x # 1. E 1 2 1 x 3 dx 5 2 (area below x-axis) 1 (area above x-axis) 5 30. The graph of f ( x ) 5 x 3 1 3 is three units higher than the graph of g ( x ) 5 x 3 . The extra area is (3)(1) 5 3. E 1 ( x 3 1 3) dx 5 } 1 4 } 1 3 5 } 1 4 3 } 31. Observe that the region under the graph of f ( x ) 5 ( x 2 2) 3 for 2 # x # 3 is just the region under the graph of...
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