Question

Consider the following 2D shapes: A) (0,4) B) (-4,-1) (0,0) (1,-1) (-2,0) (2,0) (0,-3) a) Write simplified integrals that expresses the mass of region A, given density function $\delta(x, y)$, without evaluating. (Hint: Consider which direction requires far less work): Mass(A) = b) Given a CLOCKWISE path C around the edge of region B starting at (0,-1), and vector field $\vec{F} = [xy^2, x^2]$, write simplified integrals that express the line integral: $\oint \vec{F} \cdot d\vec{r} = $

          Consider the following 2D shapes:
A) 
(0,4)
B)
(-4,-1) (0,0) (1,-1)
(-2,0) (2,0)
(0,-3)
a) Write simplified integrals that expresses the mass
of region A, given density function $\delta(x, y)$, without
evaluating. (Hint: Consider which direction requires
far less work):
Mass(A) =
b) Given a CLOCKWISE path C around the edge
of region B starting at (0,-1), and
vector field $\vec{F} = [xy^2, x^2]$, write simplified
integrals that express the line integral:
$\oint \vec{F} \cdot d\vec{r} = $

Consider the following 2D shapes:
A)
(0,4)
B)
(-4,-1) (0,0) (1,-1)
(-2,0) (2,0)
(0,-3)
a) Write simplified integrals that expresses the mass
of region A, given density function δ(x, y), without
evaluating. (Hint: Consider which direction requires
far less work):
Mass(A) =
b) Given a CLOCKWISE path C around the edge
of region B starting at (0,-1), and
vector field F⃗ = [xy^2, x^2], write simplified
integrals that express the line integral:
∮F⃗· dr⃗ =

Added by Anna F.

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