Calculate the area defined by the graph of the function $$f(x)=\dfrac{1}{1+x^2}$$ in the interval $$[-2,2]$$.
See development and solution
Development:
This function has the following graph:
To calculate the area delimited by a function and the $$x$$ axis, we calculate the integral in the given interval. In our case:
$$$\text{Area}=\int_{-2}^2 f(x) \ dx=\int_{-2}^{2} \dfrac{1}{1+x^2} \ dx = [\arctan]_{-2}^{2}=1.1071-(-1.1071)=2.2142 u^2$$$
Solution:
$$\text{Area}=2.2142 u^2$$