Search code examples
pythonsympysymbolic-integration

Area of the quarter circle with SymPy Integrate?

I would like to evaluate the following integral using SymPy:

from sympy import *
x = symbols('x')
a = symbols('a', positive=True)
expr = sqrt(a**2 - x**2)
integrate(expr, (x, 0, pi/2))

What I would expect as an outcome is the area of the quarter circle (i.e., a^2*pi/4). Unfortunately, SymPy does not provide this result. When considering

integrate(expr, x)

I obtain the correct indefinite integral but when adding the limits it does not work.

Any ideas what I am doing wrong?

Solution

  • The limit should be a if that is the radius and you are working in Cartesian coordinates:

    from sympy import *
x = symbols('x')
a = symbols('a', positive=True)
expr = sqrt(a**2 - x**2)
integrate(expr, (x, 0, a))

    That gives:

       2
π⋅a 
────
 4