def numerical(f, a, b, step):
x = a
lst = []
while x + step < b:
dy, _ = numerical_integral(f, x, x + step)
lst.append((x, dy))
x += step
return lst
def _evalf_(self, f, x, a, b, parent=None, algorithm=None):
"""
Return a numerical approximation of the integral
EXAMPLES::
sage: from sage.symbolic.integration.integral import definite_integral
sage: h = definite_integral(sin(x)*log(x)/x^2, x, 1, 2); h
integrate(log(x)*sin(x)/x^2, x, 1, 2)
sage: h.n() # indirect doctest
0.14839875208053...
TESTS:
Check if :trac:`3863` is fixed::
sage: integrate(x^2.7 * e^(-2.4*x), x, 0, 3).n()
0.154572952320790
"""
from sage.calculus.integration import numerical_integral
# The gsl routine returns a tuple, which also contains the error.
# We only return the result.
return numerical_integral(f, a, b)[0]
def _evalf_(self, f, x, a, b, parent=None, algorithm=None):
"""
Returns numerical approximation of the integral
EXAMPLES::
sage: from sage.symbolic.integration.integral import definite_integral
sage: h = definite_integral(sin(x)*log(x)/x^2, x, 1, 2); h
integrate(log(x)*sin(x)/x^2, x, 1, 2)
sage: h.n() # indirect doctest
0.14839875208053...
TESTS:
Check if :trac:`3863` is fixed::
sage: integrate(x^2.7 * e^(-2.4*x), x, 0, 3).n()
0.154572952320790
"""
from sage.calculus.integration import numerical_integral
# The gsl routine returns a tuple, which also contains the error.
# We only return the result.
return numerical_integral(f, a, b)[0]
