ρ2=cos2θ

The area enclosed by the lemniscate in the first quadrant and the X axis is equal to the area enclosed by the other three quadrants and the X axis.

So choose: a.

analyse

This topic examines the solution of plane graphic area in polar coordinate system.

The area of the plane figure enclosed by curve ρ = φ (θ) and ray θ = α and θ = β is A=∫βα 12[φ(θ)]2dθ.

Therefore, lemniscate's cartesian coordinate equation must be transformed into polar coordinate equation.

If you are not clear, please refer to the picture:

Extended data:

The Application of lemniscate

Shown is a lemniscate graphic.

In mathematics, lemniscate is a plane algebraic curve defined by the following equation in a plane rectangular coordinate system:

Where a is that length of +0 in 438 of figure 65.

Bernoulli lemniscate also has a concise expression in polar coordinates:

In bipolar coordinate system, Bernoulli lemniscate equation is similar:

App application

(1) Application in textile: Bernoulli lemniscate is widely used as a pattern in textile. The cloth woven from lemniscate has beautiful appearance, compact structure and repeated gradient.

(2) Application in supercharger: Bernoulli-lemniscate shock-free dual-intake flow-expanding supercharger is widely used in industry.

(3) Application in gambling: Bernoulli lemniscate is widely used in gambling in Jacob Bernoulli's riddle.