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