Sr Examen
Integral de 32*sin^4(x)*cos^2(x) dx
Solución
Ha introducido
[src]
pi -- 6 / | | 4 2 | 32*sin (x)*cos (x) dx | / 0
$$\int\limits_{0}^{\frac{\pi}{6}} 32 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx$$
Integral((32*sin(x)^4)*cos(x)^2, (x, 0, pi/6))
Respuesta (Indefinida)
[src]
/ | 3 3 | 4 2 5 6 6 5 16*cos (x)*sin (x) 2 4 4 2 | 32*sin (x)*cos (x) dx = C - 2*cos (x)*sin(x) + 2*x*cos (x) + 2*x*sin (x) + 2*sin (x)*cos(x) - ------------------ + 6*x*cos (x)*sin (x) + 6*x*cos (x)*sin (x) | 3 /
$$\int 32 \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}\, dx = C + 2 x \sin^{6}{\left(x \right)} + 6 x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)} + 6 x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)} + 2 x \cos^{6}{\left(x \right)} + 2 \sin^{5}{\left(x \right)} \cos{\left(x \right)} - \frac{16 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)}}{3} - 2 \sin{\left(x \right)} \cos^{5}{\left(x \right)}$$
Gráfica
Respuesta
[src]
___
\/ 3 pi
- ----- + --
2 3
$$- \frac{\sqrt{3}}{2} + \frac{\pi}{3}$$
=
=
___
\/ 3 pi
- ----- + --
2 3
$$- \frac{\sqrt{3}}{2} + \frac{\pi}{3}$$
-sqrt(3)/2 + pi/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.