Sr Examen
Integral de cos^2(3x)sin6x dx
Solución
Ha introducido
[src]
1 / | | 2 | cos (3*x)*sin(6*x) dx | / 0
$$\int\limits_{0}^{1} \sin{\left(6 x \right)} \cos^{2}{\left(3 x \right)}\, dx$$
Integral(cos(3*x)^2*sin(6*x), (x, 0, 1))
Gráfica
Respuesta
[src]
2 2 2
sin (3)*sin(6) sin (3)*cos(6) cos (3)*sin(6) cos(3)*cos(6)*sin(3) cos(3)*sin(3)*sin(6)
- -------------- - -------------- + -------------- - -------------------- + --------------------
4 6 4 2 4
$$\frac{\sin{\left(6 \right)} \cos^{2}{\left(3 \right)}}{4} - \frac{\sin^{2}{\left(3 \right)} \cos{\left(6 \right)}}{6} - \frac{\sin^{2}{\left(3 \right)} \sin{\left(6 \right)}}{4} + \frac{\sin{\left(3 \right)} \sin{\left(6 \right)} \cos{\left(3 \right)}}{4} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)} \cos{\left(6 \right)}}{2}$$
=
=
2 2 2
sin (3)*sin(6) sin (3)*cos(6) cos (3)*sin(6) cos(3)*cos(6)*sin(3) cos(3)*sin(3)*sin(6)
- -------------- - -------------- + -------------- - -------------------- + --------------------
4 6 4 2 4
$$\frac{\sin{\left(6 \right)} \cos^{2}{\left(3 \right)}}{4} - \frac{\sin^{2}{\left(3 \right)} \cos{\left(6 \right)}}{6} - \frac{\sin^{2}{\left(3 \right)} \sin{\left(6 \right)}}{4} + \frac{\sin{\left(3 \right)} \sin{\left(6 \right)} \cos{\left(3 \right)}}{4} - \frac{\sin{\left(3 \right)} \cos{\left(3 \right)} \cos{\left(6 \right)}}{2}$$
-sin(3)^2*sin(6)/4 - sin(3)^2*cos(6)/6 + cos(3)^2*sin(6)/4 - cos(3)*cos(6)*sin(3)/2 + cos(3)*sin(3)*sin(6)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.