Sr Examen
Integral de cos(2x)^2*cos(3x)^2 dx
Solución
Ha introducido
[src]
1 / | | 2 2 | cos (2*x)*cos (3*x) dx | / 0
$$\int\limits_{0}^{1} \cos^{2}{\left(2 x \right)} \cos^{2}{\left(3 x \right)}\, dx$$
Integral(cos(2*x)^2*cos(3*x)^2, (x, 0, 1))
Gráfica
Respuesta
[src]
2 2 2 2 2 2 2 2 2 2 2 2
cos (2)*cos (3) cos (2)*sin (3) cos (3)*sin (2) sin (2)*sin (3) sin (2)*cos(3)*sin(3) cos (3)*cos(2)*sin(2) 7*cos (2)*cos(3)*sin(3) 9*sin (3)*cos(2)*sin(2)
--------------- + --------------- + --------------- + --------------- - --------------------- + --------------------- + ----------------------- + -----------------------
4 4 4 4 15 40 30 40
$$\frac{\sin{\left(2 \right)} \cos{\left(2 \right)} \cos^{2}{\left(3 \right)}}{40} + \frac{7 \sin{\left(3 \right)} \cos^{2}{\left(2 \right)} \cos{\left(3 \right)}}{30} + \frac{9 \sin{\left(2 \right)} \sin^{2}{\left(3 \right)} \cos{\left(2 \right)}}{40} + \frac{\sin^{2}{\left(3 \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \sin^{2}{\left(3 \right)}}{4} - \frac{\sin^{2}{\left(2 \right)} \sin{\left(3 \right)} \cos{\left(3 \right)}}{15} + \frac{\cos^{2}{\left(2 \right)} \cos^{2}{\left(3 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \cos^{2}{\left(3 \right)}}{4}$$
=
=
2 2 2 2 2 2 2 2 2 2 2 2
cos (2)*cos (3) cos (2)*sin (3) cos (3)*sin (2) sin (2)*sin (3) sin (2)*cos(3)*sin(3) cos (3)*cos(2)*sin(2) 7*cos (2)*cos(3)*sin(3) 9*sin (3)*cos(2)*sin(2)
--------------- + --------------- + --------------- + --------------- - --------------------- + --------------------- + ----------------------- + -----------------------
4 4 4 4 15 40 30 40
$$\frac{\sin{\left(2 \right)} \cos{\left(2 \right)} \cos^{2}{\left(3 \right)}}{40} + \frac{7 \sin{\left(3 \right)} \cos^{2}{\left(2 \right)} \cos{\left(3 \right)}}{30} + \frac{9 \sin{\left(2 \right)} \sin^{2}{\left(3 \right)} \cos{\left(2 \right)}}{40} + \frac{\sin^{2}{\left(3 \right)} \cos^{2}{\left(2 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \sin^{2}{\left(3 \right)}}{4} - \frac{\sin^{2}{\left(2 \right)} \sin{\left(3 \right)} \cos{\left(3 \right)}}{15} + \frac{\cos^{2}{\left(2 \right)} \cos^{2}{\left(3 \right)}}{4} + \frac{\sin^{2}{\left(2 \right)} \cos^{2}{\left(3 \right)}}{4}$$
cos(2)^2*cos(3)^2/4 + cos(2)^2*sin(3)^2/4 + cos(3)^2*sin(2)^2/4 + sin(2)^2*sin(3)^2/4 - sin(2)^2*cos(3)*sin(3)/15 + cos(3)^2*cos(2)*sin(2)/40 + 7*cos(2)^2*cos(3)*sin(3)/30 + 9*sin(3)^2*cos(2)*sin(2)/40
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.