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unseenoi
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hi everyone can someone please help me out. This is not homework just getting ready for school
integral of sin(x^2)
integral of sin(x^2)
In that case, I would try a substitution.unseenoi said:no i am not
Well noted Cyosis, I presumed that by 'school' the OP meant grad school, which looking back now may have not been a wise assumption.Cyosis said:Seeing as you say you're getting ready for school, are you still in high school? Also I just noticed that you didn't specify an interval to integrate over. Did you just make up this integral yourself? The reason I am asking this is that this function does not have a primitive function in terms of elementary functions.
Indeed it is, as has already been pointed out.g_edgar said:[itex]\int \sin(x^2)\,dx[/itex] is not elementary.
Really? How about substituting u=x2, then expanding sin(u) about u=0 and performing term-wise integration? Does this not give the power-series definition of the Fresnel function S(x)?g_edgar said:So "hints" like "try substitution" are not helpful.
Hootenanny said:Really? How about substituting u=x2, then expanding sin(u) about u=0 and performing term-wise integration? Does this not give the power-series definition of the Fresnel function S(x)?
n!kofeyn said:I think your substitution hint implied either u-substitution or integration by parts. There is no need to make a substitution to expand sin(x2) out into its power series.
There is no systematic way to compute sine as I know.Barkan said:There is no systematic way to compute Fresnel integrals as I know.
But there are several approximation methods
The integral of sin(x^2) does not have a standard formula. It is an example of an integral that cannot be expressed in terms of elementary functions. Instead, it can be approximated using numerical methods or represented using special functions such as the Fresnel integral.
As mentioned before, the integral of sin(x^2) cannot be solved using traditional methods. However, it can be evaluated using numerical integration techniques such as the trapezoidal rule or Simpson's rule. Alternatively, it can be represented using special functions such as the Fresnel integral.
The graph of the integral of sin(x^2) is a smooth, continuous curve that oscillates around the x-axis. It has a similar shape to the graph of the sine function, but with smaller amplitude and faster oscillations.
The integral of sin(x^2) has various applications in physics, engineering, and other fields. It appears in the solution of differential equations, the calculation of electric potentials, and the analysis of diffraction patterns, to name a few examples.
As mentioned before, the integral of sin(x^2) cannot be expressed in terms of elementary functions. However, it can be represented using special functions such as the Fresnel integral, which can simplify some calculations. Additionally, approximations can be used for specific values of x or to simplify the integration process.