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1-16 Evaluate the line integral, where C is the given curve. 1. fcyds, C: x= t², y = 2t, 0≤ t ≤3

1-16 Evaluate the line integral, where C is the given curve. 1. fcyds, C: x= t², y = 2t, 0≤ t ≤3

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Eve times. 1 a (1 mis 1/200 S 16.2 EXERCISES and the 13 1-16 Evaluate the line integral, where C is the given curve. 1. fcyds, C: x = t², y = 2t, 0≤ t ≤ 3 diban P fF.dr = P dx + Qdy + R dz C C Din = x+x+in [=(+1xx For example, the integral Jey dx + z dy + x dz in Example 6 could be expressed a Sc F. dr where - ib (1)4- ((1)) C is the line segment from (2, 0) to (5, 4) 6. Sc ex dx, C is the arc of the curve x = y³ from (-1, -1) to (1, 1) DA 20 10. fey²z ds, 2. fc (x/y) ds, C: x = t³, y = t², 1 ≤ t ≤2·1=1 dC is the line segment from (3, 1, 2) to (1, 2, 5) 3. fcxy¹ds, 4. cxe' ds, 5. fc (x²y + sin x) dy, dw gan ali vd boo C is the arc of the parabola y = x² from (0, 0) to (π, TT²) = (s) [x = (32x) oder al Jedi sun llina, ei si bo nehenoizo nadw bogaerionu, su C is the right half of the circle x² + y² = 161. Sexe ³² ds, the point C is the line segment from (0, 0, 0) to (1, 2, 3) 12. fc (x² + y² + z²) ds, C: x=t, y = cos 2t, z = 2t, z = sin 2t, 0≤ t ≤2m 13. fcxye dy, C: x=t, y = t², z = 1²³, 0≤1≤1x 1435 15.0 14. fcy dx + z dy + x dz, ed C: x = √t, y=t, z = t², 1 ≤ t ≤ 4 7. S (x + 2y) dx + x² dy, C consists of line segments from (0, 0) to (2, 1) and from (2, 1) to (3, 0) 8. fcx² dx + y² dy, C consists of the arc of the circle 15 x² + y² 4 from (2,0) to (0, 2) followed by the line segment from (0, 2) to (4,3) ately F(x, y, z) = yi+zj+xk sochen- S= holoons 15-(0)7)3 where F = Pi+Qj+ Rk vas the particle along Cisapprox 9. fcx²y ds, C: x = cos t, y = sin t, z = t, 0≤t≤m/2 15. fz² dx + x² dy + y² dz, C is the line segment from (1, 0, 0) to (4, 1, 2) 16. fc (y + z) dx + (x + 2) dy + (x + y) dz, C consists of line segments from (0, 0, 0) to (1, 0, 1) and from (1, 0, 1) to (0, 1, 2) top 18 1 t 2 f 2
Transcribed Image Text:Eve times. 1 a (1 mis 1/200 S 16.2 EXERCISES and the 13 1-16 Evaluate the line integral, where C is the given curve. 1. fcyds, C: x = t², y = 2t, 0≤ t ≤ 3 diban P fF.dr = P dx + Qdy + R dz C C Din = x+x+in [=(+1xx For example, the integral Jey dx + z dy + x dz in Example 6 could be expressed a Sc F. dr where - ib (1)4- ((1)) C is the line segment from (2, 0) to (5, 4) 6. Sc ex dx, C is the arc of the curve x = y³ from (-1, -1) to (1, 1) DA 20 10. fey²z ds, 2. fc (x/y) ds, C: x = t³, y = t², 1 ≤ t ≤2·1=1 dC is the line segment from (3, 1, 2) to (1, 2, 5) 3. fcxy¹ds, 4. cxe' ds, 5. fc (x²y + sin x) dy, dw gan ali vd boo C is the arc of the parabola y = x² from (0, 0) to (π, TT²) = (s) [x = (32x) oder al Jedi sun llina, ei si bo nehenoizo nadw bogaerionu, su C is the right half of the circle x² + y² = 161. Sexe ³² ds, the point C is the line segment from (0, 0, 0) to (1, 2, 3) 12. fc (x² + y² + z²) ds, C: x=t, y = cos 2t, z = 2t, z = sin 2t, 0≤ t ≤2m 13. fcxye dy, C: x=t, y = t², z = 1²³, 0≤1≤1x 1435 15.0 14. fcy dx + z dy + x dz, ed C: x = √t, y=t, z = t², 1 ≤ t ≤ 4 7. S (x + 2y) dx + x² dy, C consists of line segments from (0, 0) to (2, 1) and from (2, 1) to (3, 0) 8. fcx² dx + y² dy, C consists of the arc of the circle 15 x² + y² 4 from (2,0) to (0, 2) followed by the line segment from (0, 2) to (4,3) ately F(x, y, z) = yi+zj+xk sochen- S= holoons 15-(0)7)3 where F = Pi+Qj+ Rk vas the particle along Cisapprox 9. fcx²y ds, C: x = cos t, y = sin t, z = t, 0≤t≤m/2 15. fz² dx + x² dy + y² dz, C is the line segment from (1, 0, 0) to (4, 1, 2) 16. fc (y + z) dx + (x + 2) dy + (x + y) dz, C consists of line segments from (0, 0, 0) to (1, 0, 1) and from (1, 0, 1) to (0, 1, 2) top 18 1 t 2 f 2
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