# Definite integrals examples

Collection of examples with solutions of definite integrals. Definite integrals are the next step in higher mathematics after indefinite integrals. In contrast to indefinite integrals which give as an integration process result a function, definite integrals give as integration process a number. When function lays in the first quater of XY plot we can interpret geometrically a definite integral of that function as an area below function's curve.

## Definite integral example 1

Solved definite integral of function f(x)=1/(3·x+5)^{1/2}. Definite integral is calculated on interval [-1,7].Theorem about integration by substitution is applied in example.

Definite integral - example 1

## Definite integral example 2

Solved definite integral of function f(x)=1/(e^{x}+e^{-x}). Definite integral is calculated on interval [ln2,ln3]. Formulas for exponents and logarithms are used. Theorem about integration by substitution is applied in example.

Definite integral - example 2
## Definite integral example 3

Solved definite integral of function f(x)=x·e^{2·x}. Definite integral is calculated on interval [0,1]. Theorem about integration by parts is applied in example.

Definite integral - example 3
## Definite integral example 4

Solved definite integral of function f(x)=x^{2}. Definite integral is calculated on interval [1,2].

Definite integral - example 4
## Definite integral example 5

Solved definite integral of function f(x)=sin(x). Definite integral is calculated on interval [0,2·π].

Definite integral - example 5
## Definite integral example 6

Solved definite integral of function f(x)=cos(x). Definite integral is calculated on interval [0,π/2].

Definite integral - example 6
## Definite integral example 7

Solved definite integral of function f(x)=x^{2}+2. Definite integral is calculated on interval [-1,3]. Theorem about integral from sum of two functions is used.

Definite integral - example 7
## Definite integral example 8

Solved definite integral of function f(x)=x^{2}+sin(x). Definite integral is calculated on interval [π,2·π]. Theorem about integral from sum of two functions is used.

Definite integral - example 8