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.
Bioprofe | Calculation of areas – Definite Integral | 01
Areas of flat regions:
Bioprofe | Calculation of areas – Definite Integral | 02 |
Bioprofe | Calculation of areas – Definite Integral | 03 |
Bioprofe | Calculation of areas – Definite Integral | 04 |
Bioprofe | Calculation of areas – Definite Integral | 05 |
Areas limited by several functions:
Bioprofe | Calculation of areas – Definite Integral | 06
This area is calculated as follows:
Bioprofe | Calculation of areas – Definite Integrals | 07 |
– |
Bioprofe | Calculation of areas – Definite Integrals | 08 |
Bioprofe | Calculation of areas – Definite Integrals | 09
Functions whose graphs are waveform:
Bioprofe | Calculation of areas – Definite Integrals | 10
Bioprofe | Calculation of areas – Definite Integrals | 11
Examples:
Area delimited by the parabola y=x² and the line y=1
Bioprofe | Calculation of areas – Definite Integrals | 12
Integration interval:
Bioprofe | Calculation of areas – Definite Integrals | 13
Therefore:
Bioprofe | Calculation of areas – Definite Integrals | 14
Area delimited by the parabola y=x², the line y=-x+2 and the ox axis
Bioprofe | Calculation of areas – Definite Integrals | 15
Points of intersection:
Bioprofe | Calculation of areas – Definite Integrals | 16
It is applied the following formula:
Bioprofe | Calculation of areas – Definite Integrals | 17
Integration interval:
x=1
x=-2
Therefore:
Bioprofe | Calculation of areas – Definite Integrals | 18
Area delimited by the parabola y=-x², the lines x=-1, x=2 and the ox axis
Bioprofe | Calculation of areas – Definite Integrals | 19
Bioprofe | Calculation of areas – Definite Integrals | 20
Area delimited by the function y=x³, the lines x=-1, x=2 and the ox axis
Bioprofe | Calculation of areas – Definite Integrals | 21
Bioprofe | Calculation of areas – Definite Integrals | 22
It is solved:
Bioprofe | Calculation of areas – Definite Integrals | 23
Area delimited by the functions y=e^x, y=e^-x , the lines x=-1, x=1 and the ox axis
Bioprofe | Calculation of areas – Definite Integrals | 24
Bioprofe | Calculation of areas – Definite Integrals | 25