Let (a) Show that P y Q x (b) Show that c F dr is not independent of path Compute c1 F dr and c2 F dr where C 1 and C 2 are the upper and lower halves of the circle x 2 y 2 1 from (1, 0) to (1, 0) Does this contradict Theorem 6 Data from Theorem 6 Let F Pi Q j be a vector field on an open simply co...

Step 1 Fxy x1x Step 2 A On comparing with Pi Q P x And Step 3 Then OP 12y x y xy2y xy x y Step ...

Let (a) Show that P/y = Q/x. (b) Show that c F dr is not

Question:

Let

F(x, y) -yi+xj x + y

(a) Show that ∂P/∂y = ∂Q/∂x.

(b) Show that ∫_c F · dr is not independent of path. [Compute ∫_c1 F · dr and ∫_c2 F · dr where C₁ and C₂ are the upper and lower halves of the circle x² + y² = 1 from (1, 0) to (–1, 0).] Does this contradict Theorem 6?

Data from Theorem 6

Let F = Pi + Q j be a vector field on an open simply-connected region D. Suppose that P and Q have continuous first-order derivatives and

aQ throughout D

Then F is conservative.

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Calculus

ISBN: 9780495011606

6th Edition

Authors: James Stewart

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Question Posted: Nov 05, 2023 04:42 AM

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Let (a) Show that P/y = Q/x. (b) Show that c F dr is not

Question:

F(x, y) -yi+xj x² + y²

Step by Step Answer:

Step 1 Fxy x1x Step 2 A On comparing with Pi Q P x And Step 3 Then OP 12y x y xy2y xy x y Step ...View the full answer

Calculus

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