Sr Examen
Integral de 1/5(sen^2)x dx
Solución
Ha introducido
[src]
1 / | | 2 | sin (x) | -------*x dx | 5 | / 0
$$\int\limits_{0}^{1} x \frac{\sin^{2}{\left(x \right)}}{5}\, dx$$
Integral((sin(x)^2/5)*x, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 2 2 2 2 2 2 | sin (x) sin (x) x *cos (x) x *sin (x) x*cos(x)*sin(x) | -------*x dx = C + ------- + ---------- + ---------- - --------------- | 5 20 20 20 10 | /
$$\int x \frac{\sin^{2}{\left(x \right)}}{5}\, dx = C + \frac{x^{2} \sin^{2}{\left(x \right)}}{20} + \frac{x^{2} \cos^{2}{\left(x \right)}}{20} - \frac{x \sin{\left(x \right)} \cos{\left(x \right)}}{10} + \frac{\sin^{2}{\left(x \right)}}{20}$$
Gráfica
Respuesta
[src]
2 2 sin (1) cos (1) cos(1)*sin(1) ------- + ------- - ------------- 10 20 10
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{10} + \frac{\cos^{2}{\left(1 \right)}}{20} + \frac{\sin^{2}{\left(1 \right)}}{10}$$
=
=
2 2 sin (1) cos (1) cos(1)*sin(1) ------- + ------- - ------------- 10 20 10
$$- \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{10} + \frac{\cos^{2}{\left(1 \right)}}{20} + \frac{\sin^{2}{\left(1 \right)}}{10}$$
sin(1)^2/10 + cos(1)^2/20 - cos(1)*sin(1)/10
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.