Integration Examples 

by 

Christopher P. Benton, Ph.D. 

 

Here are some basic integral examples using MAPLE. 

 

int(x^2, x); 1 

1/3*x^3 

int(x^2, x = 0 .. 1); 1 

1/3 

int(y^10, y); 1 

1/11*y^11 

int(y^10, y = 1 .. 2); 1 

2047/11 

evalf(%); 

186.0909091 

> int(cos(x), x); 1
 

sin(x) 

> int(cos(x), x = 0 .. 1/2*Pi); 1
 

1 

> int(cos(x), x = 0 .. 3); 1
 

sin(3) 

> evalf(%); 1
 

.1411200081 

We can also use tools from the expression pallete to enter integrals. 

 

int(x^2, x) 

1/3*x^3 

int(sqrt(x), x = 0 .. 1) 

2/3 

int(x*sqrt(x^2+1), x) 

1/3*(x^2+1)^(3/2) 

int(x*sqrt(x^2+1), x = 1 .. 5) 

-2/3*2^(1/2)+26/3*2^(1/2)*13^(1/2) 

> evalf(%); 1
 

43.24869340 

 

And finally, we can do integration with respect to particular variables and multiple integration. 

 

int(x^5*y^3, x); 1 

1/6*x^6*y^3 

int(x^5*y^3, y); 1 

1/4*x^5*y^4 

int(x^5*y^3, x = 0 .. 1); 1 

1/6*y^3 

int(x^5*y^3, y = 0 .. 1); 1 

1/4*x^5 

int(int(x^5*y^3, x = 0 .. 1), y = 0 .. 1); 1 

1/24 

int(x^5*y^3, x = y .. y^2); 1 

1/6*y^3*(y^12-y^6) 

int(int(x^5*y^3, x = y .. y^2), y = 0 .. 2); 1 

3328/5 

evalf(%); 1 

665.6000000