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Unformatted text preview: a, b ], then the area between the graphs of f and g is given by Area = A B f ( x ) âˆ’ g ( x ) dx . Ã« o When f ( x ) = x + 1 , g ( x ) = âˆ’ 1 2 x , therefore, the value of 4 ( x + 1) + 2 1 x dx Ã« o is the area of the shaded region 5. V = 1 3 Ï€ 6. V = 1 3 Explanation: The volume of the solid of revolution obtained by rotating the graph of y = f ( x ) on [ a, b ] about the xaxis is given by volume = Ï€ A B f ( x ) 2 dx . When f ( x ) = x 2 , a = 2 , b = 3 , 6 therefore, 4 . V = Ï€ 2 3 x 4 2 dx . 2 Consequently, âˆ’2 4 6 V = Ï€ Å½ âˆ’ x 4 â‚ƒ 2 3 = 3 2 Ï€ . keywords: AreaBetween, AreaBetweenExam, 003 10.0 points Find the volume, V , of the solid obtained by rotating the region bounded by y = x 2 , x = 2 , x = 3 , y =...
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 Spring '07
 Sadler
 1 g, âˆ’2, following shaded regions

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