8.2 Area of a Surface of

8.2 Area of a Surface of - 8.2 Area of a Surface of...

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Unformatted text preview: 8.2 Area of a Surface of Revolution Definition: If the graph of a continuous function is revolved about a line, the resulting surface is called a surface of revolution Axis of Revolution L 1 r 2 r ) ( 2 1 radius average segment line of length where 2 2 1 r r r L rL S + = = = = Surface Area of a Frustum of a Cone: Surface Area: = y d s S 2 If the curve is rotated about the x-axis = x d s S 2 If the curve is rotated about the y-axis Note: ) ( when 1 2 x f y dx dx dy ds = + = Use or ) ( when 1 2 y g x dy dy dx ds = + = Examples: Find the area of the surface obtained by rotating the curve about the x-axis: 1) 8 , 4 4 2 + = x x y Solutions: ( 29 ( 29 ( 29 ( 29 ( 29 2 1 0 5 3 1 6 8 4 0 3 4 3 2 2 4 4 4 2 2 w h en : L im it L o w er 6 8 w h en : L im it U p p er 4 4 4 1 1 2 2 4 1 1 U se 4 4 4 4 N o w , 2 h av e W e 2 / 3 2 / 3 6 2 2 / 3 2 2 / 1 6 2 2 6 2 2 2 2 2 2 2 2- =- = + = + = + =...
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8.2 Area of a Surface of - 8.2 Area of a Surface of...

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