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Numerical integration: Difference between revisions
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(Added C# implementation.) |
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print integrate "i.trapezium "fn2 4 -1 2 ; 2.351014
print integrate "i.simpsons "fn2 4 -1 2 ; 2.447732</lang>
=={{header|Lua}}==
<lang lua>function leftRect( f, a, b, n )
local h = (b - a) / n
local x = a
local sum = 0
for i = 1, 100 do
sum = sum + a + f(x)
x = x + h
end
return sum * h
end
function rightRect( f, a, b, n )
local h = (b - a) / n
local x = b
local sum = 0
for i = 1, 100 do
sum = sum + a + f(x)
x = x - h
end
return sum * h
end
function midRect( f, a, b, n )
local h = (b - a) / n
local x = a + h/2
local sum = 0
for i = 1, 100 do
sum = sum + a + f(x)
x = x + h
end
return sum * h
end
function trapezium( f, a, b, n )
local h = (b - a) / n
local x = a
local sum = 0
for i = 1, 100 do
sum = sum + f(x)*2
x = x + h
end
return (b - a) * sum / (2 * n)
end
function simpson( f, a, b, n )
local h = (b - a) / n
local sum1 = f(a + h/2)
local sum2 = 0
for i = 1, n-1 do
sum1 = sum1 + f(a + h * i + h/2)
sum2 = sum2 + f(a + h * i)
end
return (h/6) * (f(a) + f(b) + 4*sum1 + 2*sum2)
end
int_methods = { leftRect, rightRect, midRect, trapezium, simpson }
for i = 1, 5 do
print( int_methods[i]( function(x) return x^3 end, 0, 1, 100 ) )
print( int_methods[i]( function(x) return 1/x end, 1, 100, 1000 ) )
print( int_methods[i]( function(x) return x end, 0, 5000, 5000000 ) )
print( int_methods[i]( function(x) return x end, 0, 6000, 6000000 ) )
end</lang>
=={{header|MATLAB}}==
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