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