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Resolución de integrales/ x*sinx/ √x*sinx

Integral de √x*sinx dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |    ___          
 |  \/ x *sin(x) dx
 |                 
/                  
0
∫01xsin⁡(x) dx\int\limits_{0}^{1} \sqrt{x} \sin{\left(x \right)}\, dx 
Integral(sqrt(x)*sin(x), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                                                                               
                                                                                      _  /              |   2 \
  /                                                       5/2                        |_  |   3/4, 5/4   | -x  |
 |                                       /  ___   ___\   x   *Gamma(3/4)*Gamma(5/4)* |   |              | ----|
 |   ___                     ___   ____  |\/ 2 *\/ x |                              2  3 \3/2, 7/4, 9/4 |  4  /
 | \/ x *sin(x) dx = C + x*\/ 2 *\/ pi *S|-----------| - ------------------------------------------------------
 |                                       |     ____  |                  4*Gamma(7/4)*Gamma(9/4)                
/                                        \   \/ pi   /
∫xsin⁡(x) dx=C−x52Γ(34)Γ(54)2F3(34,5432,74,94|−x24)4Γ(74)Γ(94)+2πxS(2xπ)\int \sqrt{x} \sin{\left(x \right)}\, dx = C - \frac{x^{\frac{5}{2}} \Gamma\left(\frac{3}{4}\right) \Gamma\left(\frac{5}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{3}{4}, \frac{5}{4} \\ \frac{3}{2}, \frac{7}{4}, \frac{9}{4} \end{matrix}\middle| {- \frac{x^{2}}{4}} \right)}}{4 \Gamma\left(\frac{7}{4}\right) \Gamma\left(\frac{9}{4}\right)} + \sqrt{2} \sqrt{\pi} x S\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right)
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Trazar el gráfico f(x)
Respuesta [src] 
                                        /  ___ \           
                            ___   ____  |\/ 2  |           
                        5*\/ 2 *\/ pi *C|------|*Gamma(5/4)
                                        |  ____|           
  5*cos(1)*Gamma(5/4)                   \\/ pi /           
- ------------------- + -----------------------------------
      4*Gamma(9/4)                  8*Gamma(9/4)
−5cos⁡(1)Γ(54)4Γ(94)+52πC(2π)Γ(54)8Γ(94)- \frac{5 \cos{\left(1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)} 
=
= 
                                        /  ___ \           
                            ___   ____  |\/ 2  |           
                        5*\/ 2 *\/ pi *C|------|*Gamma(5/4)
                                        |  ____|           
  5*cos(1)*Gamma(5/4)                   \\/ pi /           
- ------------------- + -----------------------------------
      4*Gamma(9/4)                  8*Gamma(9/4)
−5cos⁡(1)Γ(54)4Γ(94)+52πC(2π)Γ(54)8Γ(94)- \frac{5 \cos{\left(1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)} 
-5*cos(1)*gamma(5/4)/(4*gamma(9/4)) + 5*sqrt(2)*sqrt(pi)*fresnelc(sqrt(2)/sqrt(pi))*gamma(5/4)/(8*gamma(9/4))
Respuesta numérica [src] 
0.364221932032132
0.364221932032132

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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