Question

(b) C is the closed curve comprised of the upper half of the circle x^2 + y^2 = 1 and the line-segment [-1, 1] on the x-axis. Using Green's Theorem or otherwise, calculate the work done by the force field F = (3xy^2 - y^3)i + (x^3 + 3x^2y)j in traversing one loop counterclockwise around C.

Name: b c is the closed curve comprised of the upper half of the circle x2 y2 1 and the line segment 1 1 on the x axis using greens theorem or otherwise calculate the work done by the force field 08456
Uploaded: 2023-07-28T08:17:43-08:00
Duration: 2 min 42 s
Channel: Collin Parker
Description: b c is the closed curve comprised of the upper half of the circle x2 y2 1 and the line segment 1 1 on the x axis using greens theorem or otherwise calculate the work done by the force field 08456

          (b) C is the closed curve comprised of the upper half of the circle x^2 + y^2 = 1
and the line-segment [-1, 1] on the x-axis.
Using Green's Theorem or otherwise, calculate the work done by the force field F = (3xy^2 - y^3)i + (x^3 + 3x^2y)j in traversing one loop counterclockwise around C.

Added by Catalina B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Collin Parker

07/28/2023

Step 1

The upper half of the circle can be parameterized as x = cos(t) and y = sin(t), where t ranges from 0 to π. The line segment on the x-axis can be parameterized as x = t and y = 0, where t ranges from -1 to 1. Show more…

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(b) C is the closed curve comprised of the upper half of the circle x^2 + y^2 = 1 and the line-segment [-1, 1] on the x-axis. Using Green's Theorem or otherwise, calculate the work done by the force field F = (3xy^2 - y^3)i + (x^3 + 3x^2y)j in traversing one loop counterclockwise around C.