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sec8_2 - 8.2 Area of Surface of Revolution 1. Surface Area...

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8.2 Area of Surface of Revolution 1. Surface Area A = πl ( r 1 + r 2 )=2 πrl The surface area of the surface obtained by rotation the curve y = f ( x )on a x b about the x -axis is approximated by n ± i =1 2 πf ( x * i ) ² 1+[ f ± ( x * i )] 2 Δ x 1
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Section 8.2 Surface Area 2 Theorem 1.1. The surface area of the surface obtained by rotation the curve y = f ( x ) on a x b about the x -axis equals The surface area of the surface obtained by rotation the curve y = f ( x ) on a x b about the y -axis equals The surface area of the surface obtained by rotation the curve x = g ( y ) on c y d about the x -axis equals The surface area of the surface obtained by rotation the curve x = g ( y ) on c y d about the y -axis equals Remark 1.1. The arc length formulas from 8.1 may be written L = ± ds = ± ² ( dx ) 2 +( dy ) 2 = ± ³ 1+ ´ dy dx µ 2 dx = ± ³ 1+ ´
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This note was uploaded on 03/14/2011 for the course MAC 2312 taught by Professor Zhang during the Fall '07 term at FSU.

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sec8_2 - 8.2 Area of Surface of Revolution 1. Surface Area...

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