3. (Areas of Surfaces of Revolution). For each of the following subproblems: (a) sketch the specified curvey; (b) sketch the surface S of revolution obtained by revolving y about the x-axis; (c) if y = (y(t), y(t)), where t runs in an interval [a, b], is a simple parametric curve, find x' = '(t) and y' = '(t) (if not, provide an appropriate parameterization of y first); (d) find x2 + y², and then find and simplify y√x² + y²; (e) find the indefinite integral [y√√¹² + y² dt; (f) find the area of S by evaluating the integral 2 (g) round your result in (f) to five decimal places. x = 5 cos³ (t/2), y = 5 sin³ (t/2), (iii) y = √11x, (0 < x < 121); (i) SUVE (0 < t < 2π); y√x¹² + y² dt; (ii) (iv) I = 10(t - sin t), = 10(1 - cost), y = x²/64+ y²/25 = 1, between y = 0 and y = 5. (0 < t < 2π);
3. (Areas of Surfaces of Revolution). For each of the following subproblems: (a) sketch the specified curvey; (b) sketch the surface S of revolution obtained by revolving y about the x-axis; (c) if y = (y(t), y(t)), where t runs in an interval [a, b], is a simple parametric curve, find x' = '(t) and y' = '(t) (if not, provide an appropriate parameterization of y first); (d) find x2 + y², and then find and simplify y√x² + y²; (e) find the indefinite integral [y√√¹² + y² dt; (f) find the area of S by evaluating the integral 2 (g) round your result in (f) to five decimal places. x = 5 cos³ (t/2), y = 5 sin³ (t/2), (iii) y = √11x, (0 < x < 121); (i) SUVE (0 < t < 2π); y√x¹² + y² dt; (ii) (iv) I = 10(t - sin t), = 10(1 - cost), y = x²/64+ y²/25 = 1, between y = 0 and y = 5. (0 < t < 2π);
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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![3. (Areas of Surfaces of Revolution). For each of the following subproblems:
(a) sketch the specified curve y;
(b) sketch the surface S of revolution obtained by revolving y about the x-axis;
(c) if y = (9(t), 4(t)), where t runs in an interval (a, b], is a simple parametric curve, find a' = o'(t) and y' = ' (t) (if
not, provide an appropriate parameterization of y first);
(d) find æ2 + y², and then find and simplify yr2 + y'²;
(e) find the indefinite integral yVa2 + y'² dt;
%3D
(f) find the area of S by evaluating the integral 27 | yV² + y'² dt;
(g) round your result in (f) to five decimal places.
x = 5 cos (t/2),
(i)
y = 5 sin°(t/2),
10(t – sin t),
(0 <t< 27);
(0 <t< 27);
(ii)
[y = 10(1 – cos t),
a2 /64 + y? /25 = 1,
(iii) y = v11£, (0 <x < 121);
(iv)
hetween y -
0 and y – 5.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01bae6af-8d02-4068-8941-fe4d9b02f893%2F936e8837-fb1d-49fe-8616-e8a03e2555b2%2Foh4njh8_processed.png&w=3840&q=75)
Transcribed Image Text:3. (Areas of Surfaces of Revolution). For each of the following subproblems:
(a) sketch the specified curve y;
(b) sketch the surface S of revolution obtained by revolving y about the x-axis;
(c) if y = (9(t), 4(t)), where t runs in an interval (a, b], is a simple parametric curve, find a' = o'(t) and y' = ' (t) (if
not, provide an appropriate parameterization of y first);
(d) find æ2 + y², and then find and simplify yr2 + y'²;
(e) find the indefinite integral yVa2 + y'² dt;
%3D
(f) find the area of S by evaluating the integral 27 | yV² + y'² dt;
(g) round your result in (f) to five decimal places.
x = 5 cos (t/2),
(i)
y = 5 sin°(t/2),
10(t – sin t),
(0 <t< 27);
(0 <t< 27);
(ii)
[y = 10(1 – cos t),
a2 /64 + y? /25 = 1,
(iii) y = v11£, (0 <x < 121);
(iv)
hetween y -
0 and y – 5.
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