Bepaalde integralen: toepassingen

F(x) = 1

F(x) = x

 $F\left(x\right)=\frac{1}{x}$  

 $F\left(x\right)=\sqrt{x}$  

 $F\left(x\right)=\frac{1}{\ln\ a}a^x$  

 $F\left(x\right)\ =\ e^x$  

 $F\left(x\right)=\ln\ x$  

 $F\left(x\right)=\ln\ \left|x\right|$  

 $\int_0^1\left(x^2-x\right)dx$  

 $\int_1^0\left(x-x^2\right)dx$  

 $\int_0^1\left(x-x^2\right)dx$  

 $\left(\frac{1}{3}x^3-\frac{1}{2}x^2\right)_0^1$  

 $\left(\frac{1}{3}x^2-\frac{1}{2}x^3\right)_0^1$  

 $\left(\frac{1}{2}x^2-\frac{1}{3}x^3\right)_1^0$  

 $\left(\frac{1}{2}x^2-\frac{1}{3}x^3\right)_0^1$  

Integratieregel lineariteit (regel 2)

Integratieregel additiviteit/optelbaarheid (regel 1)

Hoofdstelling 2

Meetkundige betekenis van de bepaalde integraal

$\int_a^b\left(g\left(x\right)-f\left(x\right)\right)dx$

$\int_a^b\left(h\left(x\right)-f\left(x\right)\right)dx$

$\int_a^b\left(f\left(x\right)-h\left(x\right)\right)dx$

$\int_a^b\left(h\left(x\right)-g\left(x\right)\right)dx$

$\int_a^b\left(g\left(x\right)-f\left(x\right)\right)dx$

$\int_a^b\left(h\left(x\right)-f\left(x\right)\right)dx$

$\int_a^b\left(f\left(x\right)-h\left(x\right)\right)dx$

$\int_a^b\left(h\left(x\right)-g\left(x\right)\right)dx$

4

3

2

1

13/6

13/9

7/6

19/6

$\int_1^2\left(l\left(y\right)-k\left(y\right)\right)dx$

$\int_1^2\left(l\left(y\right)-k\left(y\right)\right)dy$

$\int_2^1\left(l\left(y\right)-k\left(y\right)\right)dy$

$\int_1^2\left(k\left(y\right)-l\left(y\right)\right)dy$

 $\int_1^2\left(6\ -y\ -y^2\right)dy$ 

 $\int_1^2\left(6\ -y\ -y^2\right)dx$ 

 $\int_1^2\left(6\ -y\ +y^2\right)dy$ 

 $\int_2^1\left(6\ -y\ -y^2\right)dy$ 

13/6

13/9

7/6

19/6