Comment #9 on issue 1001 by [email protected]: Failure with definite integral of sqrt(R^2-x^2) and variations
http://code.google.com/p/sympy/issues/detail?id=1001
In master you can try
import sympy x=Symbol('x') R=Symbol('R', positive = True) integrate(sqrt(R**2-x**2), (x, 0, R))
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