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Karrali integrallarni hisoblash
Maple muhitida ikki va uch karali integrallarni hisoblash uchun maxsus buyruqlar mavjud. Ikki karrali integralni hisoblash uchun Doubleint(f(x, y), D) buyrug’i ishlatiladi, bu yerda D – integrallash sohasi bo’lib, quyidagi ko’rinishlardan birida yoziladi:

1. 
   x=x1..x2, y=y1..y2, bu yerda x1, x2, y1, y2 sonlar integrallashning to’rt burchakli sohasini aniqlaydi;
   
2. 
   x=f1(y)..f2(y), y=y1..y2, bu yerda f1(y), f2(y) –chiziqlar bo’lib y1 dan y2 gacha intervalda integrallash sohasini chap va o’ngdan chegaralaydi;
   
3. 
   x=x1..x2, y=g1(x)..g2(x) , bu yerda g1(y), g2(y) - chiziqlar bo’lib x1 dan x2 gacha intervalda integrallash sohasini quyi va yuqorian chegaralaydi.
   

Uch karali integrallar ni hisoblash uchun Tripleint(f(x, y, z),x, y, z, V) buyrug’i ishlatiladi, bu yerda V – integrallash sohasi.
Ikkala buyruq ham bekor qilingan amal buyrug’i hisoblanadi. Integralni sonli qiymatini olish uchun value(%) buyrug’i ishlatiladi.
Takroriy integrallarni int buyruqlarini takroran yozish orqali bajarish mumkin, masalan, takroriy integral quyidagicha hisoblanadi:
> int(int(x^2*y^3, x=0..1), y=0..2);

Misollar
1. Aniqmas integrallarni toping:
a) ;
> Int(cos(x)*cos(2*x)*cos(3*x),x)=int(cos(x)*cos(2*x)*cos(3*x), x);


b)
> Int((3*x^4+4)/(x^2*(x^2+1)^3),x)= int((3*x^4+4)/(x^2*(x^2+1)^3),x);

2. Aniq integralni hisoblang: , bu yerda a > 0, b > 0.
> assume (a>0); assume (b>0); >Int(sin(x)*cos(x)/(a^2*cos(x)^2+b^2*sin(x)^2),x=0..Pi/2)=int(sin(x)*cos(x)/(a^2*cos(x)^2+b^2*sin(x)^2),x=0..Pi/2);

3. Xosmas integralni toping: , bunda a>-1
> restart; assume(a>-1);
> Int((1-exp(-a*x^2))/(x*exp(x^2)), x=0..+infinity)=int((1-exp(-a*x^2))/(x*exp(x^2)), x=0..+infinity);

4. Integralni sonli qiymatini toping:
> Int(cos(x)/x, x=Pi/6..Pi/4)=evalf(int(cos(x)/x, x=Pi/6..Pi/4), 15);

5. Bo’laklab integrallashning barcha bosqichlarini bajaring: .
> restart; with(student): J=Int(x^3*sin(x),x);

> J=intparts(Int(x^3*sin(x),x),x^3);

> intparts(%,x^2);

> intparts(%,x);

> value(%);

6. Universal o’rniga qo’yish tg(x/2)=t bilan integralni hisoblang:
.
> J=Int(1/(1+cos(x)), x=-Pi/2..Pi/2);

> J=changevar(tan(x/2)=t,Int(1/(1+cos(x)), x=-Pi/2..Pi/2), t);

> value(%);
J=2
7. takroriy integralni hisoblang.
> Int(Int(y^3/(x^2+y^2),x=0..y),y=2..4)=
int(int(y^3/(x^2+y^2), x=0..y),y=2..4);

2. chiziqlar bilan chegaralangan ikki karrali integralni hisoblang.
Izoh: avval integrallash sohasi D ni tengsizlik ko’rinishida yozamiz:
> restart: with(student):
> J:=Doubleint(sin(x+2*y), x=y..Pi/2-y, y=0..Pi/2);

> J:=value(%);

3. uch karrali integralni hisoblang.
> J:=Tripleint(4+z, y=x^2..1,x=-1..1, z=0..2);

> J:=value(%);