# How do you find the integral of a summation?

## Question:

How do you find the integral of a summation?

## Linearity of the Integral:

The majority of operators are linear operators, the derivative operator, the integral operator, among others.

In the case of the integral, this property can be written: {eq}\int {\left( {af\left( x \right) + bg\left( x \right)} \right)dx} = a\int {f\left( x \right)dx} + b\int {g\left( x \right)dx}. {/eq}

## Answer and Explanation:

The integral operator is a linear operator, that is, considering the summation, the integral of the sum is the sum of the integrals and the constant factors can be placed outside the integral operator.

For example, we have:

{eq}\int {\left( {5x + 3} \right)dx} = 5\frac{{{x^2}}}{2} + 3x + C. {/eq}

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