Question

If curl F = (x^2 + z^2)j + 5k, find ∫ C F · dr, where C is a circle of radius 3, centered at the origin, with: (a) C is in the xy-plane, oriented counterclockwise when viewed from above. (b) C is in the xz-plane, oriented counterclockwise when viewed from the positive y-axis.

Name: if curl f x 2 z 2 j 5k find c f dr where c is a circle of radius 3 centered at the origin with a c is in the xy plane oriented counterclockwise when viewed from above b c is in the xz plane 61994
Uploaded: 2023-06-08T06:37:40-08:00
Duration: 2 min 26 s
Channel: Madhur L
Description: if curl f x 2 z 2 j 5k find c f dr where c is a circle of radius 3 centered at the origin with a c is in the xy plane oriented counterclockwise when viewed from above b c is in the xz plane 61994

          If curl F = (x^2 + z^2)j + 5k, find ∫ C F · dr, where C is a circle of radius 3, centered at the origin, with:
(a) C is in the xy-plane, oriented counterclockwise when viewed from above.
(b) C is in the xz-plane, oriented counterclockwise when viewed from the positive y-axis.

Added by John G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/08/2023

Step 1

(a) Since C is in the xy-plane and has a radius of 3, we can parameterize it as: ⃗r(t) = 3cos(t)⃗i + 3sin(t)⃗j, where 0 ≤ t ≤ 2π. (b) Since C is in the xz-plane and has a radius of 3, we can parameterize it as: ⃗r(t) = 3cos(t)⃗i + 3sin(t)⃗k, where 0 ≤ t ≤ Show more…

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If curl F = (x^2 + z^2)j + 5k, find ∫ C F · dr, where C is a circle of radius 3, centered at the origin, with: (a) C is in the xy-plane, oriented counterclockwise when viewed from above. (b) C is in the xz-plane, oriented counterclockwise when viewed from the positive y-axis.