Integration of sin x dx problem in python programming implementation

Question

I want to implement this integration in Python:

So far I did the code below but it is not making sense. What am I doing wrong?

import sympy as sm
x=sm.Symbol('x')
x=sm.integrate(math.sin(x)**2, 2*x)

Answer 1

Referencing the other answers you don't need to use trigintegrate but you do need to supply the integration limits when calling integrate if it is a definite integral:

In [31]: from sympy import integrate, sin, oo, Symbol

In [32]: x = Symbol('x')

In [33]: integrate(sin(x**2), (x, 0, oo))
Out[33]: 
√2⋅√π
─────
  4  

In [34]: _.n()
Out[34]: 0.626657068657750

Answer 2

I think you are looking for this:

import sympy as sm

x=sm.Symbol('x')
x=sm.integrate(sm.sin(x**2), x)

print(x)

You need to use the sin function from sympy lib instead of math lib.

Answer 3

One issue was that you didn't use the trig functions from sympy:

from sympy import sin
from sympy.abc import x

integrate(sm.sin(x**2), x)

This will return a complicated expression involving the Gamma function because sin(x^2) has no simple indefinite integral.

You can, however, directly compute the definite integral you are showing, simply by using the bounds as argument (and using sympy.oo for infinity):

from sympy import sin, oo
from sympy.abc import x

integrate(sin(x**2), (x, 0, oo))

This returns properly: .

(source: from the sympy documentation)

Answer 4

It helps a great deal to know what the answer is before you begin computing:

integral_0^∞ sin(x^2) dx = sqrt(π/2)/2≈0.626657