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How to use it?
- Integral of d{x}:
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Integral of x^3/sqrt(1+x^2)
- Integral of 1/x*lnx
- Integral of πdx
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Integral of -y*exp(-y/2)/2
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Identical expressions
- sin(two hundred *x^ two)
- sinus of (200 multiply by x squared )
- sinus of (two hundred multiply by x to the power of two)
- sin(200*x2)
- sin200*x2
- sin(200*x²)
- sin(200*x to the power of 2)
- sin(200x^2)
- sin(200x2)
- sin200x2
- sin200x^2
- sin(200*x^2)dx
Integral of sin(200*x^2) dx
The solution
You have entered
[src]
1 / | | / 2\ | sin\200*x / dx | / 0
$$\int\limits_{0}^{1} \sin{\left(200 x^{2} \right)}\, dx$$
Integral(sin(200*x^2), (x, 0, 1))
Detail solution
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Add the constant of integration:
FresnelSRule(a=200, b=0, c=0, context=sin(200*x**2), symbol=x)
The answer is:
The answer (Indefinite)
[src]
____ / 20*x \ / \/ pi *S|------| | | ____| | / 2\ \\/ pi / | sin\200*x / dx = C + ---------------- | 20 /
$${{\sqrt{\pi}\,\left(\left(i+1\right)\,\mathrm{erf}\left(\left(10\,i
+10\right)\,x\right)+\left(1-i\right)\,\mathrm{erf}\left(\left(10-10
\,i\right)\,x\right)+\left(1-i\right)\,\mathrm{erf}\left(5\,2^{{{3
}\over{2}}}\,\sqrt{-i}\,x\right)+\left(i+1\right)\,\mathrm{erf}
\left(5\,\left(-1\right)^{{{1}\over{4}}}\,2^{{{3}\over{2}}}\,x
\right)\right)}\over{160}}$$
The graph
The answer
[src]
____ / 20 \
3*\/ pi *S|------|*Gamma(3/4)
| ____|
\\/ pi /
-----------------------------
80*Gamma(7/4)
$${{\sqrt{\pi}\,\left(\left(i+1\right)\,\mathrm{erf}\left(10\,i+10
\right)+\left(i-1\right)\,\mathrm{erf}\left(10\,i-10\right)+\left(1-
i\right)\,\mathrm{erf}\left(5\,2^{{{3}\over{2}}}\,\sqrt{-i}\right)+
\left(i+1\right)\,\mathrm{erf}\left(5\,\left(-1\right)^{{{1}\over{4
}}}\,2^{{{3}\over{2}}}\right)\right)}\over{160}}$$
=
=
____ / 20 \
3*\/ pi *S|------|*Gamma(3/4)
| ____|
\\/ pi /
-----------------------------
80*Gamma(7/4)
$$\frac{3 \sqrt{\pi} S\left(\frac{20}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{80 \Gamma\left(\frac{7}{4}\right)}$$
The graph
Use the examples entering the upper and lower limits of integration.