Sr Examen
Integral de sin(x^2)cos(2ax) dx
Solución
Ha introducido
[src]
oo / | | / 2\ | sin\x /*cos(2*a*x) dx | / 0
$$\int\limits_{0}^{\infty} \sin{\left(x^{2} \right)} \cos{\left(2 a x \right)}\, dx$$
Integral(sin(x^2)*cos((2*a)*x), (x, 0, oo))
Respuesta (Indefinida)
[src]
/ / ___ \ / ___ \ \ / / ___ \ / ___ \ \
___ ____ | / 2\ |\/ 2 *(2*a + 2*x)| |\/ 2 *(2*a + 2*x)| / 2\| ___ ____ | / 2\ |\/ 2 *(-2*x + 2*a)| |\/ 2 *(-2*x + 2*a)| / 2\|
/ \/ 2 *\/ pi *|cos\a /*S|-----------------| - C|-----------------|*sin\a /| I*\/ 2 *\/ pi *|I*cos\a /*S|------------------| - I*C|------------------|*sin\a /|
| | | ____ | | ____ | | | | ____ | | ____ | |
| / 2\ \ \ 2*\/ pi / \ 2*\/ pi / / \ \ 2*\/ pi / \ 2*\/ pi / /
| sin\x /*cos(2*a*x) dx = C + -------------------------------------------------------------------------- - ----------------------------------------------------------------------------------
| 4 4
/
$$\int \sin{\left(x^{2} \right)} \cos{\left(2 a x \right)}\, dx = C + \frac{\sqrt{2} \sqrt{\pi} \left(- \sin{\left(a^{2} \right)} C\left(\frac{\sqrt{2} \left(2 a + 2 x\right)}{2 \sqrt{\pi}}\right) + \cos{\left(a^{2} \right)} S\left(\frac{\sqrt{2} \left(2 a + 2 x\right)}{2 \sqrt{\pi}}\right)\right)}{4} - \frac{\sqrt{2} i \sqrt{\pi} \left(- i \sin{\left(a^{2} \right)} C\left(\frac{\sqrt{2} \left(2 a - 2 x\right)}{2 \sqrt{\pi}}\right) + i \cos{\left(a^{2} \right)} S\left(\frac{\sqrt{2} \left(2 a - 2 x\right)}{2 \sqrt{\pi}}\right)\right)}{4}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.