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sin(x^2)dx
Solving integrals/ sin(x^2)dx

Integral of sin(x^2)dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |     / 2\     
 |  sin\x /*1 dx
 |              
/               
0
$$\int\limits_{0}^{1} \sin{\left(x^{2} \right)} 1\, dx$$ 
Integral(sin(x^2)*1, (x, 0, 1))
Detail solution

    FresnelSRule(a=1, b=0, c=0, context=sin(x**2)*1, symbol=x)

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
                                    /    ___\
                        ___   ____  |x*\/ 2 |
  /                   \/ 2 *\/ pi *S|-------|
 |                                  |   ____|
 |    / 2\                          \ \/ pi /
 | sin\x /*1 dx = C + -----------------------
 |                               2           
/
$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf} \left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,x}\over{2}}\right)+\left( \sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left({{\left(\sqrt{2}\,i- \sqrt{2}\right)\,x}\over{2}}\right)+\left(\sqrt{2}-\sqrt{2}\,i \right)\,\mathrm{erf}\left(\sqrt{-i}\,x\right)+\left(\sqrt{2}\,i+ \sqrt{2}\right)\,\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\, x\right)\right)}\over{16}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                /  ___ \           
    ___   ____  |\/ 2  |           
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
                |  ____|           
                \\/ pi /           
-----------------------------------
            8*Gamma(7/4)
$${{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf} \left({{\sqrt{2}\,i+\sqrt{2}}\over{2}}\right)+\left(\sqrt{2}\,i- \sqrt{2}\right)\,\mathrm{erf}\left({{\sqrt{2}\,i-\sqrt{2}}\over{2}} \right)+\left(\sqrt{2}-\sqrt{2}\,i\right)\,\mathrm{erf}\left(\sqrt{- i}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}\left( \left(-1\right)^{{{1}\over{4}}}\right)\right)}\over{16}}$$ 
=
= 
                /  ___ \           
    ___   ____  |\/ 2  |           
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
                |  ____|           
                \\/ pi /           
-----------------------------------
            8*Gamma(7/4)
$$\frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$
Упростить
Numerical answer [src] 
0.310268301723381
0.310268301723381
The graph
Integral of sin(x^2)dx dx

    Use the examples entering the upper and lower limits of integration.

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