# Integration in Maple

**Integration in Maple**

Maple int command will handle the most integrals that may be done analytically. Definite and indefinite integrals may be done, for Examples.

> int(x^2,x);

** 1/3x ^{3}**

> int(x^2,x=0..2);

**8/3**

> int(sin(4*x),x);

-**1/4cos(4x)**

> int(x*(3*x^2+2)^(5/3),x);

** 1/16(3x ^{2}+2)^{8/3}**

Remember that Maple doesn't include a constant of integration for indefinite integrals.

There are lots of integrals that can't be done analytically. ( 1 that may be done tend to appear in calculus texts. 1 that can't be done often appear in real life.) The Maple can't do an integral, this simply returns it unevaluated. example below show how to the use the evalf command to get Maple to evaluate the integral numerically.

> int(cos(x^3),x=0..1);

> evalf(int(cos(x^3),x=0..1));

The Maple uses the sophisticated numerical integration routine with automatic error control to the evaluate definite integrals that it can't do analytically. We introduce two simple numerical integration techniques that are widely used by engineers and scientists.

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