Sr Examen
Integral de (1+cos(4x))/2*(1+2cos(2x)+cos^2(2x)) dx
Solución
Ha introducido
[src]
1 / | | 1 + cos(4*x) / 2 \ | ------------*\1 + 2*cos(2*x) + cos (2*x)/ dx | 2 | / 0
$$\int\limits_{0}^{1} \frac{\cos{\left(4 x \right)} + 1}{2} \left(\left(2 \cos{\left(2 x \right)} + 1\right) + \cos^{2}{\left(2 x \right)}\right)\, dx$$
Integral(((1 + cos(4*x))/2)*(1 + 2*cos(2*x) + cos(2*x)^2), (x, 0, 1))
Gráfica
Respuesta
[src]
2 2 2 2 2 1 sin(2) cos (2) sin (2) sin(4) cos(4)*sin(2) sin (2)*cos(4) cos(2)*sin(4) cos (2)*cos(4) cos (2)*sin(4) cos(2)*sin(2) cos(2)*cos(4)*sin(2) cos(2)*sin(2)*sin(4) - + ------ + ------- + ------- + ------ - ------------- - -------------- + ------------- + -------------- + -------------- + ------------- - -------------------- + -------------------- 2 2 4 4 8 6 8 3 8 8 8 16 4
$$\frac{\sin{\left(4 \right)}}{8} + \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{8} + \frac{\sin{\left(4 \right)} \cos^{2}{\left(2 \right)}}{8} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)} \cos{\left(4 \right)}}{16} + \frac{\cos^{2}{\left(2 \right)} \cos{\left(4 \right)}}{8} + \frac{\cos^{2}{\left(2 \right)}}{4} - \frac{\sin^{2}{\left(2 \right)} \cos{\left(4 \right)}}{8} + \frac{\sin{\left(2 \right)} \sin{\left(4 \right)} \cos{\left(2 \right)}}{4} - \frac{\sin{\left(2 \right)} \cos{\left(4 \right)}}{6} + \frac{\sin{\left(4 \right)} \cos{\left(2 \right)}}{3} + \frac{\sin^{2}{\left(2 \right)}}{4} + \frac{\sin{\left(2 \right)}}{2} + \frac{1}{2}$$
=
=
2 2 2 2 2 1 sin(2) cos (2) sin (2) sin(4) cos(4)*sin(2) sin (2)*cos(4) cos(2)*sin(4) cos (2)*cos(4) cos (2)*sin(4) cos(2)*sin(2) cos(2)*cos(4)*sin(2) cos(2)*sin(2)*sin(4) - + ------ + ------- + ------- + ------ - ------------- - -------------- + ------------- + -------------- + -------------- + ------------- - -------------------- + -------------------- 2 2 4 4 8 6 8 3 8 8 8 16 4
$$\frac{\sin{\left(4 \right)}}{8} + \frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{8} + \frac{\sin{\left(4 \right)} \cos^{2}{\left(2 \right)}}{8} - \frac{\sin{\left(2 \right)} \cos{\left(2 \right)} \cos{\left(4 \right)}}{16} + \frac{\cos^{2}{\left(2 \right)} \cos{\left(4 \right)}}{8} + \frac{\cos^{2}{\left(2 \right)}}{4} - \frac{\sin^{2}{\left(2 \right)} \cos{\left(4 \right)}}{8} + \frac{\sin{\left(2 \right)} \sin{\left(4 \right)} \cos{\left(2 \right)}}{4} - \frac{\sin{\left(2 \right)} \cos{\left(4 \right)}}{6} + \frac{\sin{\left(4 \right)} \cos{\left(2 \right)}}{3} + \frac{\sin^{2}{\left(2 \right)}}{4} + \frac{\sin{\left(2 \right)}}{2} + \frac{1}{2}$$
1/2 + sin(2)/2 + cos(2)^2/4 + sin(2)^2/4 + sin(4)/8 - cos(4)*sin(2)/6 - sin(2)^2*cos(4)/8 + cos(2)*sin(4)/3 + cos(2)^2*cos(4)/8 + cos(2)^2*sin(4)/8 + cos(2)*sin(2)/8 - cos(2)*cos(4)*sin(2)/16 + cos(2)*sin(2)*sin(4)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.