## Calculation of areas – Definite Integral

# Calculation of areas – Definite Integral

Definite Integral of a function is used to calculate the areas of flat regions, which are delimited by curves and straight lines.

# Areas of flat regions:

# Areas limited by several functions:

This area is calculated as follows:

– |

# Functions whose graphs are waveform:

## Examples:

# Area delimited by the parabola **y=x²** and the line **y=1**

Integration interval:

Therefore:

# Area delimited by the parabola **y=x²**, the line **y=-x+2** and the **ox** axis

Points of intersection:

It is applied the following formula:

Integration interval:

**x=1**

**x=-2**

Therefore:

# Area delimited by the parabola **y=-x²**, the lines **x=-1**, **x=2** and the **ox** axis

# Area delimited by the function **y=x³**, the lines **x=-1**, **x=2** and the **ox** axis

It is solved:

# Area delimited by the functions **y=e^x**, **y=e^-x** , the lines **x=-1**, **x=1** and the **ox** axis

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