10.3 Parametric Arc Length & Area of a Surface of Revolution.

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Presentation transcript:

10.3 Parametric Arc Length & Area of a Surface of Revolution

OLD Arc Length:

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:

Ex 1: Find the length of the curve.

OLD Surface Area:

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:

Ex 2: Find the area of the surface obtained by rotating the curve about the x-axis:

Ex 3: Find the area of the surface obtained by rotating the curve about the y-axis:

10.3 pg. 659 #1, 3, 5, 9, 11, 21, 23, 25, & 29