Sr Examen
Integral de sin(x/2)*sin(9*x/2) dx
Solución
Ha introducido
[src]
1 / | | /x\ /9*x\ | sin|-|*sin|---| dx | \2/ \ 2 / | / 0
$$\int\limits_{0}^{1} \sin{\left(\frac{x}{2} \right)} \sin{\left(\frac{9 x}{2} \right)}\, dx$$
Integral(sin(x/2)*sin((9*x)/2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | /x\ /9*x\ sin(5*x) sin(4*x) | sin|-|*sin|---| dx = C - -------- + -------- | \2/ \ 2 / 10 8 | /
$$\int \sin{\left(\frac{x}{2} \right)} \sin{\left(\frac{9 x}{2} \right)}\, dx = C + \frac{\sin{\left(4 x \right)}}{8} - \frac{\sin{\left(5 x \right)}}{10}$$
Gráfica
Respuesta
[src]
9*cos(9/2)*sin(1/2) cos(1/2)*sin(9/2)
- ------------------- + -----------------
40 40
$$\frac{\sin{\left(\frac{9}{2} \right)} \cos{\left(\frac{1}{2} \right)}}{40} - \frac{9 \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{9}{2} \right)}}{40}$$
=
=
9*cos(9/2)*sin(1/2) cos(1/2)*sin(9/2)
- ------------------- + -----------------
40 40
$$\frac{\sin{\left(\frac{9}{2} \right)} \cos{\left(\frac{1}{2} \right)}}{40} - \frac{9 \sin{\left(\frac{1}{2} \right)} \cos{\left(\frac{9}{2} \right)}}{40}$$
-9*cos(9/2)*sin(1/2)/40 + cos(1/2)*sin(9/2)/40
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.