Sr Examen
Integral de (sin^2)x(cos^2)x dx
Solución
Ha introducido
[src]
pi -- 2 / | | 2 2 | sin (x)*x*cos (x)*x dx | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} x x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$
Integral(((sin(x)^2*x)*cos(x)^2)*x, (x, 0, pi/2))
Respuesta (Indefinida)
[src]
/ | 4 4 3 3 4 3 4 3 2 3 2 3 3 2 2 2 2 | 2 2 x*cos (x) x*sin (x) sin (x)*cos(x) x *cos (x) x *sin (x) cos (x)*sin(x) x *cos (x)*sin(x) x *sin (x)*cos(x) x *cos (x)*sin (x) 3*x*cos (x)*sin (x) | sin (x)*x*cos (x)*x dx = C - --------- - --------- - -------------- + ---------- + ---------- + -------------- - ----------------- + ----------------- + ------------------ + ------------------- | 64 64 64 24 24 64 8 8 12 32 /
$$\int x x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C + \frac{x^{3} \sin^{4}{\left(x \right)}}{24} + \frac{x^{3} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{12} + \frac{x^{3} \cos^{4}{\left(x \right)}}{24} + \frac{x^{2} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{x^{2} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{x \sin^{4}{\left(x \right)}}{64} + \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{32} - \frac{x \cos^{4}{\left(x \right)}}{64} - \frac{\sin^{3}{\left(x \right)} \cos{\left(x \right)}}{64} + \frac{\sin{\left(x \right)} \cos^{3}{\left(x \right)}}{64}$$
Gráfica
Respuesta
[src]
3 pi pi - --- + --- 128 192
$$- \frac{\pi}{128} + \frac{\pi^{3}}{192}$$
=
=
3 pi pi - --- + --- 128 192
$$- \frac{\pi}{128} + \frac{\pi^{3}}{192}$$
-pi/128 + pi^3/192
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.