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