Let R be a plane region with area A whose boundary is a piecewise smooth, simple, closed curve C . Use Green’s Theorem to prove that the centroid x ¯ , y ¯ of R is given by x ¯ = 1 2 A ∮ C x 2 d y , y ¯ = − 1 2 A ∮ C y 2 d x
Let R be a plane region with area A whose boundary is a piecewise smooth, simple, closed curve C . Use Green’s Theorem to prove that the centroid x ¯ , y ¯ of R is given by x ¯ = 1 2 A ∮ C x 2 d y , y ¯ = − 1 2 A ∮ C y 2 d x
Let R be a plane region with area A whose boundary is a piecewise smooth, simple, closed curve C. Use Green’s Theorem to prove that the centroid
x
¯
,
y
¯
of R is given by
x
¯
=
1
2
A
∮
C
x
2
d
y
,
y
¯
=
−
1
2
A
∮
C
y
2
d
x
Let the rectangular region R in z-plane which is bounded by the linesx = 0,y= 0,x= 2, y =1.
Determine the region R' of the w-plane into which Ris mapped under the transformation.
w = /2e4z +(1+ 2i).
Find the centroid of the plane region bounded by the graphs of y = x3 and x = y2
Suppose f(x, y) satisfies the basic existence and uniqueness
theorem in some rectangular region Rof the- xy- plane .
Explain why two distinct solutions of the DE y' = f (x, y)
cannot intersect or be tangent to each other at a point (x,, yo) eR.
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