Question

17.4.31 Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise. A sketch is helpful. ?_C ?4y - 2, 4x^2 - 9? ? dr, where C is the boundary of the rectangle with vertices (0,0), (2,0), (2,4), and (0,4) ?_C ?4y - 2, 4x^2 - 9? ? dr =

          17.4.31
Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise. A sketch is helpful.
?_C ?4y - 2, 4x^2 - 9? ? dr, where C is the boundary of the rectangle with vertices (0,0), (2,0), (2,4), and (0,4)
?_C ?4y - 2, 4x^2 - 9? ? dr =

17.4.31
Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise. A sketch is helpful.
?C ?4y - 2, 4x^2 - 9? ? dr, where C is the boundary of the rectangle with vertices (0,0), (2,0), (2,4), and (0,4)
?C ?4y - 2, 4x^2 - 9? ? dr =

Added by Jeffrey T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/21/2023

Step 1

Given the line integral, we have: F = <P, Q> = <0, ay - 24x> Now, we need to find the partial derivatives of P and Q with respect to x and y, respectively: ∂P/∂y = 0 ∂Q/∂x = -24 According to Green's Theorem, the line integral is equal to the double integral of Show more…

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17.4.31 Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented counterclockwise. A sketch is helpful. ∮_C (4y, 2, 4x^2 - 9) ∙ dr, where C is the boundary of the rectangle with vertices (0,0), (2,0), (2,4), and (0,4) ∮_C (4y, 2, 4x^2 - 9) ∙ dr = (Type an exact answer.)