Sr Examen
Integral de 3*sin^3(x)*(-6*sin(x)*cos^2(x)) dx
Solución
Ha introducido
[src]
pi -- 2 / | | 3 2 | 3*sin (x)*-6*sin(x)*cos (x) dx | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} - 6 \sin{\left(x \right)} \cos^{2}{\left(x \right)} 3 \sin^{3}{\left(x \right)}\, dx$$
Integral((3*sin(x)^3)*((-6*sin(x))*cos(x)^2), (x, 0, pi/2))
Respuesta (Indefinida)
[src]
/ | 6 6 5 5 2 4 4 2 | 3 2 3 3 9*x*cos (x) 9*x*sin (x) 9*sin (x)*cos(x) 9*cos (x)*sin(x) 27*x*cos (x)*sin (x) 27*x*cos (x)*sin (x) | 3*sin (x)*-6*sin(x)*cos (x) dx = C + 3*cos (x)*sin (x) - ----------- - ----------- - ---------------- + ---------------- - -------------------- - -------------------- | 8 8 8 8 8 8 /
$$\int - 6 \sin{\left(x \right)} \cos^{2}{\left(x \right)} 3 \sin^{3}{\left(x \right)}\, dx = C - \frac{9 x \sin^{6}{\left(x \right)}}{8} - \frac{27 x \sin^{4}{\left(x \right)} \cos^{2}{\left(x \right)}}{8} - \frac{27 x \sin^{2}{\left(x \right)} \cos^{4}{\left(x \right)}}{8} - \frac{9 x \cos^{6}{\left(x \right)}}{8} - \frac{9 \sin^{5}{\left(x \right)} \cos{\left(x \right)}}{8} + 3 \sin^{3}{\left(x \right)} \cos^{3}{\left(x \right)} + \frac{9 \sin{\left(x \right)} \cos^{5}{\left(x \right)}}{8}$$
Gráfica
Respuesta
[src]
-9*pi ----- 16
$$- \frac{9 \pi}{16}$$
=
=
-9*pi ----- 16
$$- \frac{9 \pi}{16}$$
-9*pi/16
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.