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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
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How to use it?
- Integral of d{x}:
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Integral of xsenx
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Integral of sin(3x^2)
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Integral of x^3-3x^2
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Integral of x/(sqrt(5-4x))
- Derivative of:
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sin(3x^2)
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Identical expressions
- sin(3x^ two)
- sinus of (3x squared )
- sinus of (3x to the power of two)
- sin(3x2)
- sin3x2
- sin(3x²)
- sin(3x to the power of 2)
- sin3x^2
- sin(3x^2)dx
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Similar expressions
- 1/(sin3x^2)
Integral of sin(3x^2) dx
The solution
You have entered
[src]
1 / | | / 2\ | sin\3*x / dx | / 0
$$\int\limits_{0}^{1} \sin{\left(3 x^{2} \right)}\, dx$$
Detail solution
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Add the constant of integration:
FresnelSRule(a=3, b=0, c=0, context=sin(3*x**2), symbol=x)
The answer is:
The answer (Indefinite)
[src]
/ ___\
___ ____ |x*\/ 6 |
/ \/ 6 *\/ pi *S|-------|
| | ____|
| / 2\ \ \/ pi /
| sin\3*x / dx = C + -----------------------
| 6
/
$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\,\sqrt{3}
\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\,
\sqrt{3}\right)\,x}\over{2}}\right)+\left(\sqrt{2}\,\sqrt{3}\,i-
\sqrt{2}\,\sqrt{3}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,
\sqrt{3}\,i-\sqrt{2}\,\sqrt{3}\right)\,x}\over{2}}\right)+\left(
\sqrt{2}\,\sqrt{3}-\sqrt{2}\,\sqrt{3}\,i\right)\,\mathrm{erf}\left(
\sqrt{3}\,\sqrt{-i}\,x\right)+\left(\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\,
\sqrt{3}\right)\,\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\,
\sqrt{3}\,x\right)\right)}\over{48}}$$
The graph
The answer
[src]
/ ___ \
___ ____ |\/ 6 |
\/ 6 *\/ pi *S|------|*Gamma(3/4)
| ____|
\\/ pi /
---------------------------------
8*Gamma(7/4)
$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\,\sqrt{3}
\right)\,\mathrm{erf}\left({{\sqrt{2}\,\sqrt{3}\,i+\sqrt{2}\,\sqrt{3
}}\over{2}}\right)+\left(\sqrt{2}\,\sqrt{3}\,i-\sqrt{2}\,\sqrt{3}
\right)\,\mathrm{erf}\left({{\sqrt{2}\,\sqrt{3}\,i-\sqrt{2}\,\sqrt{3
}}\over{2}}\right)+\left(\sqrt{2}\,\sqrt{3}-\sqrt{2}\,\sqrt{3}\,i
\right)\,\mathrm{erf}\left(\sqrt{3}\,\sqrt{-i}\right)+\left(\sqrt{2}
\,\sqrt{3}\,i+\sqrt{2}\,\sqrt{3}\right)\,\mathrm{erf}\left(\left(-1
\right)^{{{1}\over{4}}}\,\sqrt{3}\right)\right)}\over{48}}$$
=
=
/ ___ \
___ ____ |\/ 6 |
\/ 6 *\/ pi *S|------|*Gamma(3/4)
| ____|
\\/ pi /
---------------------------------
8*Gamma(7/4)
$$\frac{\sqrt{6} \sqrt{\pi} S\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$
The graph
Use the examples entering the upper and lower limits of integration.