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S= 2n f(t)√/f'(t)² +g' (t)² dt. Consider the curve x = 2cos (t), y = 2sin (t) +9 on 0 st≤2x. Complete parts (a) and (b) below. ***

S= 2n f(t)√/f'(t)² +g' (t)² dt. Consider the curve x = 2cos (t), y = 2sin (t) +9 on 0 st≤2x. Complete parts (a) and (b) below. ***

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Let C be the curve x = f(t), y = g(t), for a stsb, where f' and g' are continuous on [a, b] and C does not intersect itself, except possibly at its endpoints. If g is nonnegative on [a, b], the area of the b surface obtained by revolving C about the x-axis is S= 2n g(t) √/f'(t)2 + g'(t)2 dt. Likewise, if f is nonnegative on [a, b], then the area of the surface obtained by revolving C about the y-axis is -f2² b -S2x f(t) √/f' (1)² + g'(1)² dt. Consider the curve x = 2cos (t), y = 2sin (t) +9 on 0st≤2. Complete parts (a) and (b) below. S= (Simplify your answers.) OA. An ellipse of horizontal radius and vertical radius OB. A circle of radius centered at OC. A sphere of radius centered at OD. A line that rises from left to right with a y-intercept of b. If the curve is revolved about the x-axis, describe the shape of the surface of revolution and find the area of the surface. Start by describing the revolved shape. O An ellipse A cylinder A sphere A torus (doughnut) A circle An elliptical torus (doughnut) 0000 The area of the surface is centered at
Transcribed Image Text:Let C be the curve x = f(t), y = g(t), for a stsb, where f' and g' are continuous on [a, b] and C does not intersect itself, except possibly at its endpoints. If g is nonnegative on [a, b], the area of the b surface obtained by revolving C about the x-axis is S= 2n g(t) √/f'(t)2 + g'(t)2 dt. Likewise, if f is nonnegative on [a, b], then the area of the surface obtained by revolving C about the y-axis is -f2² b -S2x f(t) √/f' (1)² + g'(1)² dt. Consider the curve x = 2cos (t), y = 2sin (t) +9 on 0st≤2. Complete parts (a) and (b) below. S= (Simplify your answers.) OA. An ellipse of horizontal radius and vertical radius OB. A circle of radius centered at OC. A sphere of radius centered at OD. A line that rises from left to right with a y-intercept of b. If the curve is revolved about the x-axis, describe the shape of the surface of revolution and find the area of the surface. Start by describing the revolved shape. O An ellipse A cylinder A sphere A torus (doughnut) A circle An elliptical torus (doughnut) 0000 The area of the surface is centered at
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