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Integral de sqrt(x)*cos(x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                
  /                
 |                 
 |    ___          
 |  \/ x *cos(x) dx
 |                 
/                  
0                  
$$\int\limits_{0}^{1} \sqrt{x} \cos{\left(x \right)}\, dx$$
Integral(sqrt(x)*cos(x), (x, 0, 1))
Respuesta (Indefinida) [src]
                                                                                                               
                                                                                      _  /              |   2 \
  /                                                       3/2                        |_  |   1/4, 3/4   | -x  |
 |                                       /  ___   ___\   x   *Gamma(1/4)*Gamma(3/4)* |   |              | ----|
 |   ___                     ___   ____  |\/ 2 *\/ x |                              2  3 \1/2, 5/4, 7/4 |  4  /
 | \/ x *cos(x) dx = C + x*\/ 2 *\/ pi *C|-----------| - ------------------------------------------------------
 |                                       |     ____  |                  4*Gamma(5/4)*Gamma(7/4)                
/                                        \   \/ pi   /                                                         
$$\int \sqrt{x} \cos{\left(x \right)}\, dx = C - \frac{x^{\frac{3}{2}} \Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{x^{2}}{4}} \right)}}{4 \Gamma\left(\frac{5}{4}\right) \Gamma\left(\frac{7}{4}\right)} + \sqrt{2} \sqrt{\pi} x C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right)$$
Gráfica
Respuesta [src]
                                      /  ___ \           
                          ___   ____  |\/ 2  |           
                      3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
                                      |  ____|           
3*Gamma(3/4)*sin(1)                   \\/ pi /           
------------------- - -----------------------------------
    4*Gamma(7/4)                  8*Gamma(7/4)           
$$- \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sin{\left(1 \right)} \Gamma\left(\frac{3}{4}\right)}{4 \Gamma\left(\frac{7}{4}\right)}$$
=
=
                                      /  ___ \           
                          ___   ____  |\/ 2  |           
                      3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
                                      |  ____|           
3*Gamma(3/4)*sin(1)                   \\/ pi /           
------------------- - -----------------------------------
    4*Gamma(7/4)                  8*Gamma(7/4)           
$$- \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sin{\left(1 \right)} \Gamma\left(\frac{3}{4}\right)}{4 \Gamma\left(\frac{7}{4}\right)}$$
3*gamma(3/4)*sin(1)/(4*gamma(7/4)) - 3*sqrt(2)*sqrt(pi)*fresnels(sqrt(2)/sqrt(pi))*gamma(3/4)/(8*gamma(7/4))
Respuesta numérica [src]
0.531202683084515
0.531202683084515

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