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.
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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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– |
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Functions whose graphs are waveform:
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Examples:
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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You can download the App BioProfe READER to practice this theory with self-corrected exercises.
