$$\int_{}^{}{\left( Pdx + Qdy \right) = \iint_{}^{}{(\frac{\text{ϑQ}}{\text{ϑx}}}} - \frac{\text{ϑP}}{\text{ϑy}})dxdy\backslash n$$

$${\int_{}^{}{\operatorname{}{\text{xsi}n^{2}xdx = \ \frac{1}{32}(4x - sin4x)}}\backslash n}{\int_{}^{}{\operatorname{cosx}{\text{si}n^{2}xdx =}}\frac{1}{36}(cos3x - 9cosx)\backslash n}{\int_{}^{}{\operatorname{cox}{sinxdx =}}\frac{1}{36}( - 9sinx - sin3x)\backslash n}{\int_{}^{}{\operatorname{co2x}{dx =}}\frac{1}{8}(4x + sin4x)\backslash n}{\int_{}^{}{\operatorname{si2x}{dx =}}\frac{1}{8}(4x - sin4x)}$$

$$\iint_{S}^{}{F\left( x,y,z \right)ds = =}\iint_{D}^{}{F\left( x,y,f\left( x,y \right) \right)\sqrt{1 + \left( \frac{\text{ϑf}}{\text{ϑx}} \right)^{2} + \left( \frac{\text{ϑf}}{\text{ϑy}} \right)^{2}}}\text{dxdy}\backslash n$$

Równania parametryczne:
Płaszczyzna:
x=x₀+ux₁+vx₂ wekt A=(x₁,y₁,z₁)
y=y₀+uy₁+vy₂ wekt B=(x₂,y₂,z₂)
z=z₀+uz₁+vz₂
Sfera:
x=rcosucosv uϵ[0,2π] vϵ[-$\frac{\pi}{2},\frac{\pi}{2}\rbrack$
y=rsinucosv
z=rsinv
Stożek:
z=k$\sqrt{x^{2} + y^{2}}$ x² + y² <= r²
x=vcosu uϵ[0,2π]
y=vsinu vϵ[0,r]
z=kv
Paraboloida:
z=k(x² + y²) x² + y² <= r²
x=vcosu
y=vsinu
z=kv²
Powierzchnia walcowa:
x² + y² = r² 0<= z <= H
x=rcosu uϵ[0,2π]
y=rsinu vϵ[0,H]
z=v

Pole płata powierzchniowego z=z(x,y)
$\iint_{D}^{}\sqrt{1 + \left\lbrack \frac{\text{ϑz}}{\text{ϑx}} \right\rbrack^{2} + \left\lbrack \frac{\text{ϑz}}{\text{ϑy}} \right\rbrack^{2}}$dxdy
Objętość obszaru ograniczonego płatem zamkniętym zorientowanym na zewnątrz
|V|=$\frac{1}{3}_{}^{}{xdydz + ydzdx + zdxdy}$ =
= zdxdy =  xdydz =  ydzdx =