Sr Examen
Integral de sqrt(x)*cos(pi*n*x) dx
Solución
Ha introducido
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2 / | | ___ | \/ x *cos(pi*n*x) dx | / 0
$$\int\limits_{0}^{2} \sqrt{x} \cos{\left(x \pi n \right)}\, dx$$
Integral(sqrt(x)*cos((pi*n)*x), (x, 0, 2))
Respuesta (Indefinida)
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___ _ / | 2 2 2 \
/ ___ 3/2 / 1 |_ | 1/4, 3/4 | -pi *n *x |
| ___ \/ n *x * / - *Gamma(1/4)*Gamma(3/4)* | | | -----------|
| ___ ___ / 1 / ___ ___ ___\ \/ n 2 3 \1/2, 5/4, 7/4 | 4 /
| \/ x *cos(pi*n*x) dx = C + x*\/ 2 * / - *C\\/ 2 *\/ n *\/ x / - ---------------------------------------------------------------------------
| \/ n 4*Gamma(5/4)*Gamma(7/4)
/
$$\int \sqrt{x} \cos{\left(x \pi n \right)}\, dx = C - \frac{\sqrt{n} x^{\frac{3}{2}} \sqrt{\frac{1}{n}} \Gamma\left(\frac{1}{4}\right) \Gamma\left(\frac{3}{4}\right) {{}_{2}F_{3}\left(\begin{matrix} \frac{1}{4}, \frac{3}{4} \\ \frac{1}{2}, \frac{5}{4}, \frac{7}{4} \end{matrix}\middle| {- \frac{\pi^{2} n^{2} x^{2}}{4}} \right)}}{4 \Gamma\left(\frac{5}{4}\right) \Gamma\left(\frac{7}{4}\right)} + \sqrt{2} x \sqrt{\frac{1}{n}} C\left(\sqrt{2} \sqrt{n} \sqrt{x}\right)$$
Respuesta
[src]
___ / ___\ ___
3*\/ 2 *S\2*\/ n /*Gamma(3/4) 3*\/ 2 *Gamma(3/4)*sin(2*pi*n)
- ----------------------------- + ------------------------------
3/2 4*pi*n*Gamma(7/4)
8*pi*n *Gamma(7/4)
$$\frac{3 \sqrt{2} \sin{\left(2 \pi n \right)} \Gamma\left(\frac{3}{4}\right)}{4 \pi n \Gamma\left(\frac{7}{4}\right)} - \frac{3 \sqrt{2} S\left(2 \sqrt{n}\right) \Gamma\left(\frac{3}{4}\right)}{8 \pi n^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}$$
=
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___ / ___\ ___
3*\/ 2 *S\2*\/ n /*Gamma(3/4) 3*\/ 2 *Gamma(3/4)*sin(2*pi*n)
- ----------------------------- + ------------------------------
3/2 4*pi*n*Gamma(7/4)
8*pi*n *Gamma(7/4)
$$\frac{3 \sqrt{2} \sin{\left(2 \pi n \right)} \Gamma\left(\frac{3}{4}\right)}{4 \pi n \Gamma\left(\frac{7}{4}\right)} - \frac{3 \sqrt{2} S\left(2 \sqrt{n}\right) \Gamma\left(\frac{3}{4}\right)}{8 \pi n^{\frac{3}{2}} \Gamma\left(\frac{7}{4}\right)}$$
-3*sqrt(2)*fresnels(2*sqrt(n))*gamma(3/4)/(8*pi*n^(3/2)*gamma(7/4)) + 3*sqrt(2)*gamma(3/4)*sin(2*pi*n)/(4*pi*n*gamma(7/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.