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 = [2r 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 a b S= = [2n f(t) √ 1 (t)² + g' (t)² dt. a Consider the curve x = 3cos (t), y = 3sin (t) + 6 on 0 st≤ 2. Complete parts (a) and (b) below. a. Describe the curve. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) OA. A circle of radius OB. A sphere of radius OC. An ellipse of horizontal radius and vertical radius 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 A torus (doughnut) O A cylinder O A circle OA sphere O An ellipse centered at centered at .... centered at
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 = [2r 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 a b S= = [2n f(t) √ 1 (t)² + g' (t)² dt. a Consider the curve x = 3cos (t), y = 3sin (t) + 6 on 0 st≤ 2. Complete parts (a) and (b) below. a. Describe the curve. Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answers.) OA. A circle of radius OB. A sphere of radius OC. An ellipse of horizontal radius and vertical radius 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 A torus (doughnut) O A cylinder O A circle OA sphere O An ellipse centered at centered at .... centered at
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 =
b
S= 2n f(t) √/f'(t)² + g'(t)² dt.
a
Consider the curve x = 3cos (t), y = 3sin (t) + 6 on 0st≤ 2. Complete parts (a) and (b) below.
0 0 0 0 0
a. Describe the curve. Select the correct choice below and fill in the answer box(es) to complete your choice.
(Simplify your answers.)
OA. A circle of radius
OB. A sphere of radius
OC. An ellipse of horizontal radius and vertical radius
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.
A torus (doughnut)
A cylinder
A circle
= 2x 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
a
A sphere
An ellipse
centered at
centered at
centered at](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8f5bee2-dbbb-4a9f-8d01-98c94e2807c2%2Fd7da0094-1090-4251-9988-9630f0eab0a9%2Fk61cgnk_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 =
b
S= 2n f(t) √/f'(t)² + g'(t)² dt.
a
Consider the curve x = 3cos (t), y = 3sin (t) + 6 on 0st≤ 2. Complete parts (a) and (b) below.
0 0 0 0 0
a. Describe the curve. Select the correct choice below and fill in the answer box(es) to complete your choice.
(Simplify your answers.)
OA. A circle of radius
OB. A sphere of radius
OC. An ellipse of horizontal radius and vertical radius
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.
A torus (doughnut)
A cylinder
A circle
= 2x 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
a
A sphere
An ellipse
centered at
centered at
centered at
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