Evaluating $\pi$ by direct integration

Question Q8.2.3

Use scipy.integrate.dblquad to evaluate $\pi$ by integration of the constant function $f(x,y)=4$ over the quarter circle with unit radius in the quadrant $x>0$, $y>0$.

Solution Q8.2.3

In [x]: from scipy.integrate import dblquad
In [x]: dblquad(lambda y, x: 4, 0, 1, lambda x: 0, lambda x: np.sqrt(1-x**2))
Out[x]: (3.1415926535897922, 3.533564552071766e-10)