sec8_2

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

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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 ) 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 = ( dx ) 2 + ( dy ) 2 = 1 + dy dx 2 dx = 1 + dx
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