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