Area of the quarter circle with SymPy Integrate?

Question

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?

Asked By: VK88

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Source

Answer 1

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

Answered By: Oscar Benjamin

Area of the quarter circle with SymPy Integrate?

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