CALCULUS PRESENTED BY GUO CHENG GUANG（06-02）

How to find the area of circle using integrations in calculs? The equation of the circle is x^2+y^2=R^2 and the circle is asymmetric with respect to the x-axis and y-axis, so first, we can solve the area of one quarter of circle and then multiple by 4 in order to get the total area of the circle.

In this video, we used three ways to integrate the area of the circle:

1. By circumference

2. By horizontal bar

3. By vertical bar

Calculus--Indefinite Integrals (06-02,S/N: 325) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

METHODS OF LIMIT-CALCULATING PRESENTED BY GUO CHENG GUANG AND GUO CHENGX...

We can use substition to the limit towards one point whenever the function is continuous at that point, that's one of the definition of continuity.If the function is not continuous at the point we can't get the limit by direct substitution.

Find limits of functions at specific points just easily by directly plugging the point into the function.

METHODS OF LIMIT-CALCULATING PRESENTED BY GUO CHENG GUANG AND GUO CHENGXI(1-02，S/N: 71) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

CALCULUS PRESENTED BY GUO CHENG GUANG（06-01）

Integral can be used to find displacement, areas, volumes, central points and other concepts that arise by combining infinitesimal date.

A definite integral is an integral with upper and lower limits, in other words it has start and end end values or there is an interval.

Calculus--Indefinite Integrals (06-01,S/N: 324) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-10)

Locus is if a point moves on a plane satisfying some given geometrical condition then the path trace out by the point in the plane.

The equation to the locus of the moving point is  the algebraic form of the given geometrical condition which is satisfy by the coordinate of all points on the locus.

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-10,S/N: 10) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

METHODS OF LIMIT-CALCULATING PRESENTED BY GUO CHENG GUANG AND GUO CHENGX...

Using direct substituion with limits: It's easily find limits of functions at points where the functions are continuous, simly plug in the value into the function.

METHODS OF LIMIT-CALCULATING PRESENTED BY GUO CHENG GUANG AND GUO CHENGXI(7-01，S/N: 70) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-09)

Five techniques to find area of a triangle:

1.shoelace formula

2.Heron's formula or Hero's formula

3.law of sines: a half of absinC

4.Cross Product

5.area of a triangle: a half of base times high【A=(1/2)bh】

ANALYTIC GEOMETRY PRESENTED BY GUO CHENG GUANG and GUO CHENGXI(01-09,S/N: 9) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated.

CALCULUS PRESENTED BY GUO CHENG GUANG（05-58）

Three methods to integrate ∫(sin(x))^2(cos(x))^4.

1.double/half angle formulae【sin(x))^2=(1-cos2x)/2,(cos(x))^2=(1+cos2x)/2)】

2.double/half angle formulae【sin2x=2sinxcosx,(cos(x))^2=(1+cos2x)/2)】

3.complex variable【z=cosθ+isinθ,z+1/z=2cosθ】

Calculus--Indefinite Integrals (05-58,S/N: 323) Presented By Guo Cheng Guang (aged 11) and Guo Chengxi (aged 8) in English. Lessons In Mathematics and Science (Physics, Chemistry and Biology) From Primary to University Presented By Guo Cheng Guang and Guo Chengxi In English. Your comment or suggestion is very much appreciated. https://www.youtube.com/channel/UC2dG5T9SJkUFTy-h0KbVbkw