So, I wanted to calculate the $\pi$, and I know that $\pi$ is the area of a circle its radius is 1, so I used this equation : $x^2 + y^2 = 1$ to get the half circle function : $f(x)=\sqrt{1-x^2}$ and that is the upper half of the circle, and then I want to get the $\pi$ from multiplying the area of this funtion (integral of it) by 2, so, it is like that :
$$\pi = 2\int_{-1}^{+1}{\sqrt{1-x^2}}\,dx$$
But the problem is I don't know how to integrate such function, if any one can help me, thanks.
