Sr Examen
Integral de xsin^2(x)x dx
Solución
Ha introducido
[src]
1 / | | 2 | x*sin (x)*x dx | / 0
$$\int\limits_{0}^{1} x x \sin^{2}{\left(x \right)}\, dx$$
Integral((x*sin(x)^2)*x, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 2 2 3 2 3 2 2 | 2 x*cos (x) x*sin (x) cos(x)*sin(x) x *cos (x) x *sin (x) x *cos(x)*sin(x) | x*sin (x)*x dx = C - --------- + --------- + ------------- + ---------- + ---------- - ---------------- | 4 4 4 6 6 2 /
$$\int x x \sin^{2}{\left(x \right)}\, dx = C + \frac{x^{3} \sin^{2}{\left(x \right)}}{6} + \frac{x^{3} \cos^{2}{\left(x \right)}}{6} - \frac{x^{2} \sin{\left(x \right)} \cos{\left(x \right)}}{2} + \frac{x \sin^{2}{\left(x \right)}}{4} - \frac{x \cos^{2}{\left(x \right)}}{4} + \frac{\sin{\left(x \right)} \cos{\left(x \right)}}{4}$$
Gráfica
Respuesta
[src]
2 2
cos (1) 5*sin (1) cos(1)*sin(1)
- ------- + --------- - -------------
12 12 4
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{4} - \frac{\cos^{2}{\left(1 \right)}}{12} + \frac{5 \sin^{2}{\left(1 \right)}}{12}$$
=
=
2 2
cos (1) 5*sin (1) cos(1)*sin(1)
- ------- + --------- - -------------
12 12 4
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{4} - \frac{\cos^{2}{\left(1 \right)}}{12} + \frac{5 \sin^{2}{\left(1 \right)}}{12}$$
-cos(1)^2/12 + 5*sin(1)^2/12 - cos(1)*sin(1)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.