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-- Numerical integration
import Numeric.GSL
quad f a b = fst $ integrateQAGS 1E-9 100 f a b
-- A multiple integral can be easily defined using partial application
quad2 f y1 y2 g1 g2 = quad h y1 y2
where
h y = quad (flip f y) (g1 y) (g2 y)
volSphere r = 8 * quad2 (\x y -> sqrt (r*r-x*x-y*y))
0 r (const 0) (\x->sqrt (r*r-x*x))
-- wikipedia example
exw = quad2 f 7 10 (const 11) (const 14)
where
f x y = x**2 + 4*y
main = do
print $ quad (\x -> 4/(x^2+1)) 0 1
print pi
print $ volSphere 2.5
print $ 4/3*pi*2.5**3
print $ exw
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