# 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.

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# Areas of flat regions:

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# Areas limited by several functions:

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This area is calculated as follows:

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# Functions whose graphs are waveform:

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

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Integration interval:

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Therefore:

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

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Points of intersection:

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It is applied the following formula:

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Integration interval:
x=1
x=-2

Therefore:

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

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

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It is solved:

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# 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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