Sr Examen
Integral de cos(3x^2+4) dx
Solución
Ha introducido
[src]
1 / | | / 2 \ | cos\3*x + 4/ dx | / 0
$$\int\limits_{0}^{1} \cos{\left(3 x^{2} + 4 \right)}\, dx$$
Integral(cos(3*x^2 + 4), (x, 0, 1))
Solución detallada
-
Añadimos la constante de integración:
FresnelCRule(a=3, b=0, c=4, context=cos(3*x**2 + 4), symbol=x)
Respuesta:
Respuesta (Indefinida)
[src]
/ / ___\ / ___\ \
___ ____ | |x*\/ 6 | |x*\/ 6 | |
/ \/ 6 *\/ pi *|cos(4)*C|-------| - S|-------|*sin(4)|
| | | ____| | ____| |
| / 2 \ \ \ \/ pi / \ \/ pi / /
| cos\3*x + 4/ dx = C + ----------------------------------------------------
| 6
/
$$\int \cos{\left(3 x^{2} + 4 \right)}\, dx = C + \frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6} x}{\sqrt{\pi}}\right)\right)}{6}$$
Gráfica
Respuesta
[src]
/ / ___ \ / ___ \ \
___ ____ | |\/ 6 | |\/ 6 | |
\/ 6 *\/ pi *|cos(4)*C|------| - S|------|*sin(4)|
| | ____| | ____| |
\ \\/ pi / \\/ pi / /
--------------------------------------------------
6
$$\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right)\right)}{6}$$
=
=
/ / ___ \ / ___ \ \
___ ____ | |\/ 6 | |\/ 6 | |
\/ 6 *\/ pi *|cos(4)*C|------| - S|------|*sin(4)|
| | ____| | ____| |
\ \\/ pi / \\/ pi / /
--------------------------------------------------
6
$$\frac{\sqrt{6} \sqrt{\pi} \left(\cos{\left(4 \right)} C\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right) - \sin{\left(4 \right)} S\left(\frac{\sqrt{6}}{\sqrt{\pi}}\right)\right)}{6}$$
sqrt(6)*sqrt(pi)*(cos(4)*fresnelc(sqrt(6)/sqrt(pi)) - fresnels(sqrt(6)/sqrt(pi))*sin(4))/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.