Defined areas under a function

Calculate the area defined by the graph of the function $f(x)=\dfrac{1}{1+x^2}$ in the interval $[-2,2]$.

This function has the following graph:

10-1-21221233

To calculate the area delimited by a function and the $x$ axis, we calculate the integral in the given interval. In our case:

$$\text{Area}=\int_{-2}^2 f(x) \ dx=\int_{-2}^{2} \dfrac{1}{1+x^2} \ dx = [\arctan]_{-2}^{2}=1.1071-(-1.1071)=2.2142 u^2$$

$$\text{Area}=2.2142 u^2$$

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