Double Integral Examples

Indefinite Integral

f[x_,y_]:=Sin[x]*Cos[y]^2;

Integrate[Integrate[f[x,y],y],x]

∫∫f[x,y]\[DifferentialD]x\[DifferentialD]y

Definite Integral w/ Constant Limits

Integrate[Integrate[f[x,y],{y,0,Pi/2}],{x,0,Pi}]

(∫_0^π)(∫_0^(π/2))f[x,y]\[DifferentialD]y\[DifferentialD]x

Indefinite Integral w/ Variable Limits

Integrate[Integrate[f[x,y],{y,0,x}],x]

∫(∫_0^x)f[x,y]\[DifferentialD]y\[DifferentialD]x

Indefinite Integral w/ Variable Limits

Integrate[Integrate[f[x,y],{y,0,x}],{x,0,Pi/2}]

(∫_0^(π/2))(∫_0^x)f[x,y]\[DifferentialD]y\[DifferentialD]x