quiz 10 onward

Question 1

how do you solve a work integral without any thrms?

Answer 1

∫ Pdx +Qdy. a ≤ t ≤ b
c

Question 2

how do you solve a flux integral without any thrms?

Answer 2

like a normal surface integral. then take η = <g_x, g_y, -1> then dot product that with the vector field. Then a normal double integral.

Question 3

State Greens Thrm

Answer 3

Let F = <P, Q> be a continuous vector field
Let C be a positively oriented simple closed curve bounding the region D.
Then ∫ F * dr = ∫∫(∂Q/∂x - ∂P/∂y)dA
c D

Question 4

State Divergence Thrm

Answer 4

Let E ⊆ R^3 whose boundary surface S is ortiented out.
Let F = <P, Q, R> be a continuous vector field
Then ∫∫F*ds = ∫ ∫ ∫ (div F) dV
S E

Question 5

what is div F?

Answer 5

div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z