Sr Examen
Integral de cos(3x)sin(x)^3 dx
Solución
Ha introducido
[src]
1 / | | 3 | cos(3*x)*sin (x) dx | / 0
$$\int\limits_{0}^{1} \sin^{3}{\left(x \right)} \cos{\left(3 x \right)}\, dx$$
Integral(cos(3*x)*sin(x)^3, (x, 0, 1))
Gráfica
Respuesta
[src]
3 3 3 3 2 2 2 1 cos (1)*sin(3) sin (1)*cos(3) cos (1)*cos(3) 3*sin (1)*sin(3) 3*cos (1)*cos(3)*sin(1) 3*sin (1)*cos(1)*sin(3) sin (1)*cos(1)*cos(3) - -- + -------------- + -------------- + -------------- + ---------------- - ----------------------- - ----------------------- + --------------------- 24 8 8 24 8 8 8 4
$$\frac{\sin^{2}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{4} + \frac{\sin^{3}{\left(1 \right)} \cos{\left(3 \right)}}{8} - \frac{1}{24} - \frac{3 \sin^{2}{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{8} + \frac{\cos^{3}{\left(1 \right)} \cos{\left(3 \right)}}{24} + \frac{\sin{\left(3 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \sin^{3}{\left(1 \right)} \sin{\left(3 \right)}}{8} - \frac{3 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{8}$$
=
=
3 3 3 3 2 2 2 1 cos (1)*sin(3) sin (1)*cos(3) cos (1)*cos(3) 3*sin (1)*sin(3) 3*cos (1)*cos(3)*sin(1) 3*sin (1)*cos(1)*sin(3) sin (1)*cos(1)*cos(3) - -- + -------------- + -------------- + -------------- + ---------------- - ----------------------- - ----------------------- + --------------------- 24 8 8 24 8 8 8 4
$$\frac{\sin^{2}{\left(1 \right)} \cos{\left(1 \right)} \cos{\left(3 \right)}}{4} + \frac{\sin^{3}{\left(1 \right)} \cos{\left(3 \right)}}{8} - \frac{1}{24} - \frac{3 \sin^{2}{\left(1 \right)} \sin{\left(3 \right)} \cos{\left(1 \right)}}{8} + \frac{\cos^{3}{\left(1 \right)} \cos{\left(3 \right)}}{24} + \frac{\sin{\left(3 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \sin^{3}{\left(1 \right)} \sin{\left(3 \right)}}{8} - \frac{3 \sin{\left(1 \right)} \cos^{2}{\left(1 \right)} \cos{\left(3 \right)}}{8}$$
-1/24 + cos(1)^3*sin(3)/8 + sin(1)^3*cos(3)/8 + cos(1)^3*cos(3)/24 + 3*sin(1)^3*sin(3)/8 - 3*cos(1)^2*cos(3)*sin(1)/8 - 3*sin(1)^2*cos(1)*sin(3)/8 + sin(1)^2*cos(1)*cos(3)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.