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Solving integrals/ sin(y^2)

Integral of sin(y^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

  1. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
                                  /    ___\
                      ___   ____  |y*\/ 2 |
  /                 \/ 2 *\/ pi *S|-------|
 |                                |   ____|
 |    / 2\                        \ \/ pi /
 | sin\y / dy = C + -----------------------
 |                             2           
/
$$\int \sin{\left(y^{2} \right)}\, dy = C + \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} y}{\sqrt{\pi}}\right)}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
                /  ___ \           
    ___   ____  |\/ 2  |           
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
                |  ____|           
                \\/ pi /           
-----------------------------------
            8*Gamma(7/4)
$$\frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$ 
=
= 
                /  ___ \           
    ___   ____  |\/ 2  |           
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
                |  ____|           
                \\/ pi /           
-----------------------------------
            8*Gamma(7/4)
$$\frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$ 
3*sqrt(2)*sqrt(pi)*fresnels(sqrt(2)/sqrt(pi))*gamma(3/4)/(8*gamma(7/4))
Numerical answer [src] 
0.310268301723381
0.310268301723381

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

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