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10.3 Parametric Arc Length & Area of a Surface of Revolution
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OLD Arc Length:
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Arc Length: if a curve C given by x = f(t), y = g(t), ≤ t ≤ , where f and g are continuous on [ , ], and C is traversed exactly once as t increases from to , then the length of the curve is:
![Arc Length: if a curve C given by x = f(t), y = g(t), ≤ t ≤ , where f and g are continuous on [ , ], and C is traversed exactly once as t increases from to , then the length of the curve is:](http://images.slideplayer.com./32/10086445/slides/slide_3.jpg "Arc Length: if a curve C given by x = f(t), y = g(t), ≤ t ≤ , where f and g are continuous on [ , ], and C is traversed exactly once as t increases from to , then the length of the curve is:")
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Ex 1: Find the length of the curve.
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OLD Surface Area:
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Surface Area: if a curve C given by x = f(t), y = g(t), ≤ t ≤ , is rotated about the x -axis where f and g are continuous on [ , ] and g(t) 0, then the area of the surface is:
![Surface Area: if a curve C given by x = f(t), y = g(t), ≤ t ≤ , is rotated about the x -axis where f and g are continuous on [ , ] and g(t) 0, then the area of the surface is:](http://images.slideplayer.com./32/10086445/slides/slide_6.jpg "Surface Area: if a curve C given by x = f(t), y = g(t), ≤ t ≤ , is rotated about the x -axis where f and g are continuous on [ , ] and g(t) 0, then the area of the surface is:")
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Ex 2: Find the area of the surface obtained by rotating the curve about the x-axis:
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Ex 3: Find the area of the surface obtained by rotating the curve about the y-axis:
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10.3 pg. 659 #1, 3, 5, 9, 11, 21, 23, 25, & 29
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