- #1
esisk
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How do I integrate sin(x^2) please?
Not (sin(x))^2. Thanks again
Not (sin(x))^2. Thanks again
How do I integrate sin(x^2) please? Not (sin(x))^2.
- Thread starter esisk
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In summary, to integrate sin(x^2), use the equality sin(u) = \frac{e^{iu}-e^{-iu}}{2i} and replace u with x^2. However, the resulting integral cannot be expressed in terms of elementary functions. This is true for most integrals and difficulty should not be a factor in integration.
- #2
Char. Limit
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Use a certain equality of the sine function, namely...
[tex]sin(u) = \frac{e^{iu}-e^{-iu}}{2i}[/tex]
Replace u with x^2 and you're good to go, assuming you know erf(x) and erfi(x).
- #3
HallsofIvy
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In other words, the integral cannot be done in terms of elementary functions.
- #4
Char. Limit
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HallsofIvy said:
But that's true for most integrals. I used to freak out when I couldn't solve an integral in terms of elementary functions, but I know better now.
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JJacquelin
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- #6
HallsofIvy
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Actually, it is true for "almost all" functions!Char. Limit said:
- #7
tauchatri
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esisk said:
hey this function is not integerable
- #8
HallsofIvy
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esisk said:
Non-sense. It is continuous, therefore it is integrable. It is simply not integrable in terms of elementary functions.tauchatri said:
- #9
tauchatri
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HallsofIvy said:
i only mean that you duffer.it's not easy to integrate
- #10
Char. Limit
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tauchatri said:
Difficulty really shouldn't matter with integration, I mean, this function isn't easy to integrate either:
[tex]\frac{sin(x^2) tan(x^3)}{x}+3 x^2 log(x) sin(x^2) sec^2(x^3)+2 x log(x) cos(x^2) tan(x^3)[/tex]
But we can still express the integral in terms of elementary functions.
FAQ: How do I integrate sin(x^2) please? Not (sin(x))^2.
1. What is the general formula for integrating sin(x^2)?
The general formula for integrating sin(x^2) is ∫sin(x^2)dx = (1/2)√(π/2)erfi(x/√2) + C, where erfi(x) is the imaginary error function.
2. Can sin(x^2) be integrated using basic integration techniques?
No, sin(x^2) cannot be integrated using basic integration techniques such as substitution or integration by parts. It requires more advanced techniques such as the use of special functions.
3. Is there a specific method for integrating sin(x^2)?
Yes, there are several methods for integrating sin(x^2), including the use of the Fresnel sine integral, the imaginary error function, and the Gaussian quadrature method.
4. What are the limits of integration for sin(x^2)?
The limits of integration for sin(x^2) depend on the specific problem or integral being solved. They can range from -∞ to +∞ or any other specified values.
5. Can technology be used to integrate sin(x^2)?
Yes, technology such as calculators and computer software can be used to numerically integrate sin(x^2) using numerical integration methods such as the trapezoidal rule or Simpson's rule.