Integral de sin(x*x) dx

Ha introducido [src]

  b            
  /            
 |             
 |  sin(x*x) dx
 |             
/              
a

$$\int\limits_{a}^{b} \sin{\left(x x \right)}\, dx$$

Integral(sin(x*x), (x, a, b))

Solución detallada

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

Añadimos la constante de integración:

$\frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}+ \mathrm{constant}$

Respuesta:

$\frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}+ \mathrm{constant}$

Respuesta (Indefinida) [src]

                                   /    ___\
                       ___   ____  |x*\/ 2 |
                     \/ 2 *\/ pi *S|-------|
  /                                |   ____|
 |                                 \ \/ pi /
 | sin(x*x) dx = C + -----------------------
 |                              2           
/

$$\int \sin{\left(x x \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}$$

Simplificar

Respuesta [src]

                  /    ___\                              /    ___\           
      ___   ____  |a*\/ 2 |                  ___   ____  |b*\/ 2 |           
  3*\/ 2 *\/ pi *S|-------|*Gamma(3/4)   3*\/ 2 *\/ pi *S|-------|*Gamma(3/4)
                  |   ____|                              |   ____|           
                  \ \/ pi /                              \ \/ pi /           
- ------------------------------------ + ------------------------------------
              8*Gamma(7/4)                           8*Gamma(7/4)

$$- \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} a}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} b}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$

=

                  /    ___\                              /    ___\           
      ___   ____  |a*\/ 2 |                  ___   ____  |b*\/ 2 |           
  3*\/ 2 *\/ pi *S|-------|*Gamma(3/4)   3*\/ 2 *\/ pi *S|-------|*Gamma(3/4)
                  |   ____|                              |   ____|           
                  \ \/ pi /                              \ \/ pi /           
- ------------------------------------ + ------------------------------------
              8*Gamma(7/4)                           8*Gamma(7/4)

$$- \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} a}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} b}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)}$$

-3*sqrt(2)*sqrt(pi)*fresnels(a*sqrt(2)/sqrt(pi))*gamma(3/4)/(8*gamma(7/4)) + 3*sqrt(2)*sqrt(pi)*fresnels(b*sqrt(2)/sqrt(pi))*gamma(3/4)/(8*gamma(7/4))

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Integral de sin(x*x) dx

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