| We have now the formula for definite integral calculus. Once we have found a primitive g(x) of function to integrate f(x), we obtain the definite integral between a and b bounds calculating the difference between g(b) and g(a) values that the primitive function reaches at bounds of integration limits. |
b |
| The difference g(b)-g(a) is often written as : [g(x)] |
a |
| b | b |
|
So we can write: |
òf(t)dt = |
[g(x)] |
| a | a |
| We know, for example, the derivative of F(x)=sin(x) function be f(x) = cos(x). So sin(x) is a primitive of cos(x). In order to calculate the definite integral of cos(x) function between a=0 and b=p/2, we will apply the theorem of Torricelli, calculating the difference between the two values that the primitive reaches in the points b and a. |
| p/2 | p/2 |
|
| òcos(t)dt = [sin(x)] | = sin(p/2) - sin(0) = 1 | |
| 0 | 0 |
|