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. ***
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F844281c0-c621-44a5-8564-9e61584c69dd%2Ffed5c2a7-6fbc-450f-b223-f8396a829251%2Fpn5qssp_processed.jpeg&w=3840&q=75)
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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