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Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (2,0,0) to (2,0,4). a. The line segment x = 2, y = 0, 0≤z≤4 b.The helix r(t) = (2cos t)i + (2sin t)j + · (²¹)K c. The x-axis from (2,0,0) to (0,0,0) followed by the parabola z = x², y = 0 from (0,0,0) to (2,0,4) (2,0,0) O B. k, Osts 2n OA. ((x²+y)i + (y² + x)j + ze²k) • dr + (0,0,0) (2,0,0) c. Choose the correct integral below to compute the work done by F along the x-axis from followed by the parabola Z=x². (2,0,4) (2,0,4) (2,0,4) (2,0,4) (2,0,0) oc. S ((x² + y)i + (y² + x)j) .dr + (ze²k).dr (²-0-²-0--I) (0,0,0) (2,0,0) Z (2,0,0) (0,0,0) (0,0,0) (0,0,0) ((x² + y)i + (y² + x)j + ze²k) •dr + S ((x² +y)i + (y² +x)j +ze²k) • dr (2,0,0) ((x² + y)i + (y² + x)j + ze²k) • dr (0,0,0) (2,0,4) D. [_ ((x²+y)i + (y² + x)j + ze²k) •dr + √ ((x² + y)i + (y² + x)j + ze³k) • dr

Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (2,0,0) to (2,0,4). a. The line segment x = 2, y = 0, 0≤z≤4 b.The helix r(t) = (2cos t)i + (2sin t)j + · (²¹)K c. The x-axis from (2,0,0) to (0,0,0) followed by the parabola z = x², y = 0 from (0,0,0) to (2,0,4) (2,0,0) O B. k, Osts 2n OA. ((x²+y)i + (y² + x)j + ze²k) • dr + (0,0,0) (2,0,0) c. Choose the correct integral below to compute the work done by F along the x-axis from followed by the parabola Z=x². (2,0,4) (2,0,4) (2,0,4) (2,0,4) (2,0,0) oc. S ((x² + y)i + (y² + x)j) .dr + (ze²k).dr (²-0-²-0--I) (0,0,0) (2,0,0) Z (2,0,0) (0,0,0) (0,0,0) (0,0,0) ((x² + y)i + (y² + x)j + ze²k) •dr + S ((x² +y)i + (y² +x)j +ze²k) • dr (2,0,0) ((x² + y)i + (y² + x)j + ze²k) • dr (0,0,0) (2,0,4) D. [_ ((x²+y)i + (y² + x)j + ze²k) •dr + √ ((x² + y)i + (y² + x)j + ze³k) • dr

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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The work done by F over the two curves is?

Find the work done by F = (x² + y)i + (y² +x)j + ze²k over the following paths from (2,0,0) to (2,0,4). a. The line segment x = 2, y = 0, 0≤z≤4 b. The helix r(t) = (2cos t)i + (2sin t)j + 2t π c. The x-axis from (2,0,0) to (0,0,0) followed by the parabola z = x², y = 0 from (0,0,0) to (2,0,4) B. k, Osts 2 (2,0,0) O A. S ((x² + y)i + (y² + x)j + ze²k) •dr + (0,0,0) O D. (2,0,0) S ((x² + y)i + (y² + x)j + ze²k) •dr + (2,0,4) (2,0,0) (2,0,4) 06. Il-3-1²-30 I Oc. (2,0,0) c. Choose the correct integral below to compute the work done by F along the x-axis from followed by the parabola Z=x² S ((x² + y)i + (y² + x) ₁) •dr + (ze²k). dr (0,0,0) (0,0,0) √ ((x² + y)i + (y² + x)j +ze²k) • dr + (2,0,0) (2,0,4) (2,0,4) Z=X (0,0,0) Z (2,0,0) (2,0,4) √((x² + y)i + (y² + x)j + ze²k) • dr (0,0,0) (0,0,0) √((x² + y)i + (y² + x)j + ze²k) • dr (2,0,0) (0,0,0) ((x² + y) + (x²+x) ₁+z6²k) .dr
Transcribed Image Text:Find the work done by F = (x² + y)i + (y² +x)j + ze²k over the following paths from (2,0,0) to (2,0,4). a. The line segment x = 2, y = 0, 0≤z≤4 b. The helix r(t) = (2cos t)i + (2sin t)j + 2t π c. The x-axis from (2,0,0) to (0,0,0) followed by the parabola z = x², y = 0 from (0,0,0) to (2,0,4) B. k, Osts 2 (2,0,0) O A. S ((x² + y)i + (y² + x)j + ze²k) •dr + (0,0,0) O D. (2,0,0) S ((x² + y)i + (y² + x)j + ze²k) •dr + (2,0,4) (2,0,0) (2,0,4) 06. Il-3-1²-30 I Oc. (2,0,0) c. Choose the correct integral below to compute the work done by F along the x-axis from followed by the parabola Z=x² S ((x² + y)i + (y² + x) ₁) •dr + (ze²k). dr (0,0,0) (0,0,0) √ ((x² + y)i + (y² + x)j +ze²k) • dr + (2,0,0) (2,0,4) (2,0,4) Z=X (0,0,0) Z (2,0,0) (2,0,4) √((x² + y)i + (y² + x)j + ze²k) • dr (0,0,0) (0,0,0) √((x² + y)i + (y² + x)j + ze²k) • dr (2,0,0) (0,0,0) ((x² + y) + (x²+x) ₁+z6²k) .dr
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