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sin(4x^2)
Solving integrals/ sin(4x^2)

Integral of sin(4x^2) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1             
  /             
 |              
 |     /   2\   
 |  sin\4*x / dx
 |              
/               
0
∫01sin⁡(4x2) dx\int\limits_{0}^{1} \sin{\left(4 x^{2} \right)}\, dx 
Integral(sin(4*x^2), (x, 0, 1))
Detail solution

    FresnelSRule(a=4, b=0, c=0, context=sin(4*x**2), symbol=x)

  1. Add the constant of integration:

    2πS(22xπ)4+constant\frac{\sqrt{2} \sqrt{\pi} S\left(\frac{2 \sqrt{2} x}{\sqrt{\pi}}\right)}{4}+ \mathrm{constant}

The answer is:

2πS(22xπ)4+constant\frac{\sqrt{2} \sqrt{\pi} S\left(\frac{2 \sqrt{2} x}{\sqrt{\pi}}\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
                                    /      ___\
                        ___   ____  |2*x*\/ 2 |
  /                   \/ 2 *\/ pi *S|---------|
 |                                  |    ____ |
 |    /   2\                        \  \/ pi  /
 | sin\4*x / dx = C + -------------------------
 |                                4            
/
∫sin⁡(4x2) dx=C+2πS(22xπ)4\int \sin{\left(4 x^{2} \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{2 \sqrt{2} x}{\sqrt{\pi}}\right)}{4}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
                /    ___\           
    ___   ____  |2*\/ 2 |           
3*\/ 2 *\/ pi *S|-------|*Gamma(3/4)
                |   ____|           
                \ \/ pi /           
------------------------------------
           16*Gamma(7/4)
32πS(22π)Γ(34)16Γ(74)\frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{2 \sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{16 \Gamma\left(\frac{7}{4}\right)} 
=
= 
                /    ___\           
    ___   ____  |2*\/ 2 |           
3*\/ 2 *\/ pi *S|-------|*Gamma(3/4)
                |   ____|           
                \ \/ pi /           
------------------------------------
           16*Gamma(7/4)
32πS(22π)Γ(34)16Γ(74)\frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{2 \sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{16 \Gamma\left(\frac{7}{4}\right)}
Упростить
Numerical answer [src] 
0.402388244671878
0.402388244671878
The graph
Integral of sin(4x^2) dx

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

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