Question

to find (x − y) dx (x y) dy c directly, we must parameterize c. since c is a circle with radius 8 centered at the origin, then a parameterization is the following. (use t as the independent variable.) x

Answer 1

The parameterize is  128 $\pi$

In mathematics, and extra in particular in geometry, parametrization (or parameterization; additionally parameterization, parametrization) is the method of locating parametric equations of a curve, a surface, or, greater typically, a manifold or an expansion, described by using an implicit equation.

"To parameterize" by means of itself method "to specific in terms of parameters". Parametrization is a mathematical technique that includes expressing the state of a system, system, or model as a feature of some independent portions referred to as parameters.

Instance 1. find a parametrization of the road through the points (three,1,2) and (1,0,5). answer: the road is parallel to the vector v=(3,1,2)−(1,0,five)=(2,1,−3). subsequently, a parametrization for the line is x=(1,0,five)+t(2,1,−3)for−∞

volume by both the methods

Directly step

{(n-y) dx+(x+y) by = √(3 co

{{(x-y)dx+(x+y) by =

ts-8 sin(t)) (8 sinct) df

t=o + (8 cost+ 8 sinds) 8 cast, dt]

25

(64 cosit,sin (4) +64 sin'? (+ 64 cs) +64 cost) sint) at

205

-(ou (ents) cost() dt = } 64 dt =64() ?

+

=

64 (211-0)

=1281

using Green's Thoerem. Step (2)

- §pdxxQdy = SS (2(244) - 2. (214) G

Jy

D

dA

=

SSC- (U)dA= [[2dA = 2 [SdA

D

D

=24

=2 182

where (A=112 area of the

= 128 $\pi$

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