How do you calculate the perimeter of this curve equation?

(0, 3), =3cos is outside.

3, 2), =1+cos The outer two curves are symmetrical with respect to the polar axis, so that only half of the upper polar axis is required to s=2 (0, 3)1+cos d +2 ( 3, 2)3cos d

Let the polar coordinate equation of the cardioid line be =a(1-cos), then the perimeter of the cardioid line is c=8a.

The derivation process is as follows.

c=∫(r^2+r'2) (1 2)d Where, r'Denotes the derivative of r, with an upper integral limit of 2 and a lower bound of 0

c=∫^(1/2)dθ

a*∫[2+2cosθ)^1/2)dθ

2a*∫|cos(θ/2)|d = 2a*[cos(2)d (upper limit is 0) + cos(2)d (lower limit is , upper limit is 2)]

8aExtended Materials

The expressions for the planar Cartesian coordinate system equations for the cardioid line are x 2+y 2+a*x=a*sqrt(x 2+y 2) and x 2+y 2-a*x=a*sqrt(x 2+y 2).

The polar equation for the cardioid line is:

Horizontal: =a(1-cos) or =a(1+cos) a>0).

Vertical: =a(1-sin ) or =a(1+sin ) a>0).

The parametric equation for the cardioid line is:

pi<=t<=pi or 0<=t<=2*pi

x=a*(2*cos(t)-cos(2*t))

y=a*(2*sin(t)-sin(2*t))

The enclosed area is 3 2*pi*a 2, and the arc length formed is 8a

The arc length element ds= (dx 2+dy2), the polar parameter equation x=rcos, y=rsin, note that r is a function of , dx=(r'(θ)cosθ-r(θ)sinθ)dθ，dy=(r'( )sin +r( )cos )d, bring it back to simplify, you can get the arc length microelement under polar coordinates, and then integrate. Of course, the increment can also be directly analyzed in polar coordinates, and some arcs can be treated as straight lines when the change is very small, and the same arc length microelement can also be obtained.

The formula for the perimeter of the heart-shaped line.

r=a(1+cosθ)(a>0)

c=∫(r^2+r'2) (1 2)d Where, r'Denotes the derivative of r, with an upper integral limit of 2 and a lower bound of 0

c=∫^(1/2)dθ

a*∫[2+2cosθ)^1/2)dθ=2a*∫|cos(θ/2)|d = 2a * [ cos( 2)d (upper limit is , lower limit is 0) + cos( 2)d (lower limit is , upper limit is 2)] = 8a

1. Create a new layer.

2. Use the Ellipse Marquee tool to draw an elliptical selection.

3. Stroke the selection.

4. Use the eraser to erase the middle part of the upper edge.

5. Use the Pen Tool to draw triangles and stroke paths.

Pa + PB + Ab = 10, and Ab = 4, get.

(x+2) 2+y 2]+ x-2) 2+y 2]=6 shift: [x+2) 2+y 2]=6- [x-2) 2+y 2]squared: (x+2) 2+y 2=36-12 [(x-2) 2+y 2]+(x-2) 2+y 2

Simplify: 3-2x 3= [(x-2) 2+y 2]Resquare: 9-4x+4x 2 9=(x-2) 2+y 2Simplify: x 2 9+y 2 5=1

The sphere is two-dimensional, and the parametric equation requires two independent parameters, and this given equation has only one parameter, and the equation of one parameter is the equation of the curve, which is the circumference. If you think about it, suppose that z's is the fixed value, that is, the intersection line with the plane of z, but only two points are determined, not a curve, and if it is a sphere, then the intersection line with the plane of z-fixed value should be a circle instead of two points. Because this given equation is an oblique circumference.

You're asking too much of a question.

One is to split the irregular shape into multiple regular diagrams and chains, and then calculate the perimeter.

The second is to know the curve equation of the graph limit and solve it by calculus.

First Quadrant.

x>0,y>0

So x+y=2

Similarly, the second quadrant is -x+y=2

The third quadrant is -x-y=2

The fourth quadrant is x-y=2

So it's a square.

Because the absolute value of the intercept is 2

i.e. the diagonal is 4

So the side length is 2 2

So the circumference is 8 2

The area is 8

This graphic actually is.

x+y=2 x-y=2 -x+y=2 -x-y=2 -x-y=2

The side length is 2 2, so the area is 8 and the perimeter is 8 2

Rectangle Area Length Width Circumference Length Width 2 Square Area Side Length Side Length Perimeter Side Length 4

Parallelogram Area Base Height Perimeter Sum of two adjacent sides 2 Circle Area Pi Radius 0 5 Perimeter 2 Pi Radius.

Fan row area (central angle 360) pi radius 0 5 perimeter 2 radius central angle pi radius 180