Sr Examen
Integral de 2/pi*x^2*(cos(x))^2 dx
Solución
Ha introducido
[src]
pi -- 2 / | | 2 2 2 | --*x *cos (x) dx | pi | / -pi ---- 2
$$\int\limits_{- \frac{\pi}{2}}^{\frac{\pi}{2}} \frac{2}{\pi} x^{2} \cos^{2}{\left(x \right)}\, dx$$
Integral(((2/pi)*x^2)*cos(x)^2, (x, -pi/2, pi/2))
Respuesta (Indefinida)
[src]
/ 2 2 3 2 3 2 2 \ / | x*sin (x) cos(x)*sin(x) x*cos (x) x *cos (x) x *sin (x) x *cos(x)*sin(x)| | 2*|- --------- - ------------- + --------- + ---------- + ---------- + ----------------| | 2 2 2 \ 4 4 4 6 6 2 / | --*x *cos (x) dx = C + ---------------------------------------------------------------------------------------- | pi pi | /
$$\int \frac{2}{\pi} x^{2} \cos^{2}{\left(x \right)}\, dx = C + \frac{2 \left(\frac{x^{3} \sin^{2}{\left(x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(x \right)}}{6} + \frac{x^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{2} - \frac{x \sin^{2}{\left(x \right)}}{4} + \frac{x \cos^{2}{\left(x \right)}}{4} - \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{4}\right)}{\pi}$$
Gráfica
Respuesta
[src]
/ 3 \ / 3\
| pi pi| | pi pi |
2*|- --- + --| 2*|- -- + ---|
\ 48 8 / \ 8 48/
- -------------- + --------------
pi pi
$$- \frac{2 \left(- \frac{\pi^{3}}{48} + \frac{\pi}{8}\right)}{\pi} + \frac{2 \left(- \frac{\pi}{8} + \frac{\pi^{3}}{48}\right)}{\pi}$$
=
=
/ 3 \ / 3\
| pi pi| | pi pi |
2*|- --- + --| 2*|- -- + ---|
\ 48 8 / \ 8 48/
- -------------- + --------------
pi pi
$$- \frac{2 \left(- \frac{\pi^{3}}{48} + \frac{\pi}{8}\right)}{\pi} + \frac{2 \left(- \frac{\pi}{8} + \frac{\pi^{3}}{48}\right)}{\pi}$$
-2*(-pi^3/48 + pi/8)/pi + 2*(-pi/8 + pi^3/48)/pi
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.