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In Exercises 11-14, a planar curve Cis given along with a sur- face f that is defined over C. Set up the line integral f(s) ds, then approximate its value using technology. 11. Cis the portion of the parabola y = the surface is f(x, y) x +2y. 2x + x + 1 on [0, 1]; %3D %3D 12. Cis the portion of the curve y = sin x on [0, 7); the surface is f(x, y) = x. 13. Cis the ellipse given by r(t) = (2 cos t, sin t) on [0, 27]; the surface is f(x, y) = 10 – x² - y. 14. Cis the portion of y x on [-1, 1); the surface is f(x, y) 2x + 3y +5. %3D

In Exercises 11-14, a planar curve Cis given along with a sur- face f that is defined over C. Set up the line integral f(s) ds, then approximate its value using technology. 11. Cis the portion of the parabola y = the surface is f(x, y) x +2y. 2x + x + 1 on [0, 1]; %3D %3D 12. Cis the portion of the curve y = sin x on [0, 7); the surface is f(x, y) = x. 13. Cis the ellipse given by r(t) = (2 cos t, sin t) on [0, 27]; the surface is f(x, y) = 10 – x² - y. 14. Cis the portion of y x on [-1, 1); the surface is f(x, y) 2x + 3y +5. %3D

Advanced Engineering Mathematics
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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#12 and #14 please!

In Exercises 11-14, a planar curve Cis given along with a sur- face f that is defined over C. Set up the line integral f(s) ds, then approximate its value using technology. 11. Cis the portion of the parabola y = 2x +x +1 on 0, 1); the surface is f(x, y) = x + 2y. %3D 12. Cis the portion of the curve y = sin x on [0, 7); the surface is f(x, y) = x. 13. Cis the ellipse given by 7(t) = (2 cos t, sin t) on [0, 27); the surface is f(x, y) = 10 – x² – y. %3D 14. Cis the portion of y = x on [-1, 1); the surface is f(x, y) = 2x + Зу + 5.
Transcribed Image Text:In Exercises 11-14, a planar curve Cis given along with a sur- face f that is defined over C. Set up the line integral f(s) ds, then approximate its value using technology. 11. Cis the portion of the parabola y = 2x +x +1 on 0, 1); the surface is f(x, y) = x + 2y. %3D 12. Cis the portion of the curve y = sin x on [0, 7); the surface is f(x, y) = x. 13. Cis the ellipse given by 7(t) = (2 cos t, sin t) on [0, 27); the surface is f(x, y) = 10 – x² – y. %3D 14. Cis the portion of y = x on [-1, 1); the surface is f(x, y) = 2x + Зу + 5.
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