Question

Let C be the circle of radius 3 about the origin traversed counterclockwise. Consider the line integral ∮C (x^2+y^2+2y)dx+(x^2-y^2)dy. a.) Is the vector field in the integral conservative? b.) Use Green's theorem to write the line integral as a double integral. Don't forget to indicate the region for the double integral. c.) Use polar coordinates to evaluate the double integral.

Name: let c be the circle of radius 3 about the origin traversed counterclockwise consider the line integral integralc x2y22ydxx2 y2dy a is the vector field in the integral conservative b use gree 03262
Uploaded: 2023-03-28T06:01:44-08:00
Duration: 4 min 20 s
Channel: Sri K
Description: let c be the circle of radius 3 about the origin traversed counterclockwise consider the line integral integralc x2y22ydxx2 y2dy a is the vector field in the integral conservative b use gree 03262

          Let C be the circle of radius 3 about the origin traversed counterclockwise. Consider the line integral ∮C (x^2+y^2+2y)dx+(x^2-y^2)dy.
a.) Is the vector field in the integral conservative?
b.) Use Green's theorem to write the line integral as a double integral. Don't forget to indicate the region for the double integral.
c.) Use polar coordinates to evaluate the double integral.

Added by Salvador M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

03/28/2023

Step 1

) To check if the vector field is conservative, we need to find the curl of the vector field. The given vector field is $\vec{F} = (x^2+y^2+2y)\hat{i} + (x^2-y^2)\hat{j}$. The curl of a vector field is given by: $$\nabla \times \vec{F} = Show more…

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Let C be the circle of radius 3 about the origin traversed counterclockwise. Consider the line integral ∮C (x^2+y^2+2y)dx+(x^2-y^2)dy. a.) Is the vector field in the integral conservative? b.) Use Green's theorem to write the line integral as a double integral. Don't forget to indicate the region for the double integral. c.) Use polar coordinates to evaluate the double integral.