1. Newton-Leibniz formula, also known as the basic formula of calculus.

2. Green's formula transforms the closed curve integral into the double integral in the region, that is, the double integral of the divergence of the plane vector field.

3. Gaussian formula divides the surface area into triple integrals in the region, which is the triple integral of the divergence of the plane vector field.

4. Stokes formula, related to curl

(2) Calculus commonly used formula:

Dx sin x=cos x

cos x = -sin x

tan x = sec2 x

cot x = -csc2 x

sec x = sec x tan x

csc x = -csc x cot x

sin x dx = -cos x + C

cos x dx = sin x + C

tan x dx = ln |sec x | + C

cot x dx = ln |sin x | + C

sec x dx = ln |sec x + tan x | + C

csc x dx = ln |csc x - cot x | + C

sin- 1(-x) = -sin- 1 x

cos- 1(-x) = - cos- 1 x

tan- 1(-x) = -tan- 1 x

cot- 1(-x) = - cot- 1 x

sec- 1(-x) = - sec- 1 x

csc- 1(-x) = - csc- 1 x

Dx sin- 1 ()=

cos- 1 ()=

tan- 1 ()=

cot- 1 ()=

sec- 1 ()=

CSC- 1(x/a)= 1

sin- 1x dx = x sin- 1x ++ C

cos- 1x dx = x cos- 1x-+C

tan- 1x dx = x tan- 1x-ln( 1+x2)+C

cot- 1x dx = x cot- 1x+ln( 1+x2)+C

sec- 1x dx = x sec- 1x-ln | x+|+C

CSC- 1x dx = x CSC- 1x+ln | x+|+C

sinh- 1 ()= ln (x+) xR

cosh- 1 ()=ln (x+) x≥ 1

tanh- 1 ()=ln () |x| 1

sech- 1()= ln(+)0≤x≤ 1

csch- 1()= ln(+)| x | & gt； 0

Dx sinh x = cosh x

cosh x = sinh x

tanh x = sech2 x

coth x = -csch2 x

sech x = -sech x tanh x

csch x = -csch x coth x

sinh x dx = cosh x + C

cosh x dx = sinh x + C

tanh x dx = ln | cosh x |+ C

coth x dx = ln | sinh x | + C

sech x dx = -2tan- 1 (e-x) + C

csch x dx = 2 ln || + C

duv = udv + vdu

duv = uv = udv + vdu

→ udv = uv - vdu

cos2θ-sin2θ=cos2θ

cos2θ+ sin2θ= 1

cosh2θ-sinh2θ= 1

cosh2θ+sinh2θ=cosh2θ

Dx sinh- 1()=

cosh- 1()=

tanh- 1()=

coth- 1()=

sech- 1()=

csch- 1(x/a)= 1

sinh- 1x dx = x sinh- 1x-+C

cosh- 1 x dx = x

tanh- 1 x dx = x tanh- 1 x+ln | 1-x2 |+C

coth- 1x dx = x coth- 1x-ln | 1-x2 |+C

sech- 1x dx = x sech- 1x-sin- 1x+C

csch- 1x dx = x csch- 1x+sinh- 1x+C

sin 3θ=3sinθ-4sin3θ

cos3θ=4cos3θ-3cosθ

→sin3θ= (3sinθ-sin3θ)

→cos3θ= (3cosθ+cos3θ)

sin x = cos x =

sinh x = cosh x =

Sine Theorem: = ==2R

Cosine Theorem: a2=b2+c2-2bc cosα

b2=a2+c2-2ac cosβ

c2=a2+b2-2ab cosγ

sin (α β)=sin α cos β cos α sin β

cos (α β)=cos α cos β sin α sin β

2 sin α cos β = sin (α+β) + sin (α-β)

2 cos α sin β = sin (α+β) - sin (α-β)

2 cos α cos β = cos (α-β) + cos (α+β)

2 sin α sin β = cos (α-β) - cos (α+β)

sin α + sin β = 2 sin (α+β) cos (α-β)

sin α - sin β = 2 cos (α+β) sin (α-β)

cos α + cos β = 2 cos (α+β) cos (α-β)

cos α - cos β = -2 sin (α+β) sin (α-β)

tan (α β)=，cot(αβ)= 1

ex = 1+x++…++……

sin x = x-+-+…++ …

cos x = 1-+-++

ln ( 1+x) = x-+-++

tan- 1 x = x-+-++

( 1+x)r = 1+rx+x2+x3+- 1 = n

= n (n+ 1)

= n (n+ 1)(2n+ 1)

= [ n (n+ 1)]2

γ(x)= x- 1e-t dt = 22x- 1dt = x- 1dt

β(m，n)= m- 1( 1-x)n- 1 dx = 22m- 1x cos2n- 1x dx = dx