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 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

Then F is conservative.

Transcribed Image Text:

F(x, y) -yi+xj x² + y²