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Unformatted text preview: a ≥ 0 the area of the region bounded by the curves x = 0 , x = a, y = 0 , and y = g ( x ) is a 3 3 , what is the area of the surface generated by revolving the curve y = Z x g ( t ) dt, 1 ≤ x ≤ 2 about the xaxis? 4. Let f ( x ) be a positive continuously diﬀerentiable function on [1 , ∞ ] . For any a > 1 , let: A ( a ) = the area of the region bounded by the curves x = 1 , x = a, y = 0 , and y = f ( x ); L ( a ) = the length of the curve y = f ( x ) from x = 1 to x = a ; S ( a ) = the area of the surface obtained by rotating about the xaxis the curve y = f ( x ) from x = 1 to x = a ; V ( a ) = the volume of the solid obtained by rotating about the xaxis the region bounded by the curves x = 1 , x = a, y = 0 , and y = f ( x ) . Show that d 2 V da 2 dL da = d 2 A da 2 dS da . 1...
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This note was uploaded on 10/29/2010 for the course MATH 112 taught by Professor Ahmetguloglu during the Spring '10 term at Bilkent University.
 Spring '10
 AhmetGuloglu
 Math, Calculus, Real Numbers

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