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2. (Chapter 17, Section 19.1) Consider the intersection R between the two circles $$x^2 + y^2 = 2$$ and $$(x - 2)^2 + y^2 = 2$$. y R x (a) Find a 2-dimensional vector field $$F = (M(x, y), N(x, y))$$ such that $$\frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} = 1$$. (3) (b) Using this F and Green's theorem (Theorem 19.1.1), write the area integral $$\iint_R 1 dA$$ as a line integral. [Hint: Any function $$y = f(x)$$ can be parametrised by $$r(t) = (t, f(t))$$. This can be used to parametrise the lines]. (4) (c) Using this line integral, find the area of R. (9)

Name: 2 chapter 17 section 191 consider the intersection r between the two circles x2 y2 2 and x 22 y2 2 y r x a find a 2 dimensional vector field f mx y nx y such that fracpartial npartial x frac 07687
Uploaded: 2022-10-07T03:42:45-08:00
Duration: 5 min 20 s
Channel: Sri K
Description: 2 chapter 17 section 191 consider the intersection r between the two circles x2 y2 2 and x 22 y2 2 y r x a find a 2 dimensional vector field f mx y nx y such that fracpartial npartial x frac 07687

          2. (Chapter 17, Section 19.1)
Consider the intersection R between the two circles $$x^2 + y^2 = 2$$ and $$(x - 2)^2 + y^2 = 2$$.
y
R
x
(a) Find a 2-dimensional vector field $$F = (M(x, y), N(x, y))$$ such that
$$\frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} = 1$$.
(3)
(b) Using this F and Green's theorem (Theorem 19.1.1), write the area integral $$\iint_R 1 dA$$ as a line integral.
[Hint: Any function $$y = f(x)$$ can be parametrised by $$r(t) = (t, f(t))$$. This can be used to parametrise the lines].
(4)
(c) Using this line integral, find the area of R.
(9)

$2 chapter 17 section 191 consider the intersection r between the two circles x2 y2 2 and x 22 y2 2 y r x a find a 2 dimensional vector field f mx y nx y such that fracpartial npartial x frac 07687$

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