Sr Examen
Integral de -48*(sin(t))^4*(cos(t))^2 dx
Solución
Ha introducido
[src]
pi -- 6 / | | 4 2 | -48*sin (t)*cos (t) dt | / pi -- 2
$$\int\limits_{\frac{\pi}{2}}^{\frac{\pi}{6}} - 48 \sin^{4}{\left(t \right)} \cos^{2}{\left(t \right)}\, dt$$
Integral((-48*sin(t)^4)*cos(t)^2, (t, pi/2, pi/6))
Respuesta (Indefinida)
[src]
/ | | 4 2 6 6 5 5 3 3 2 4 4 2 | -48*sin (t)*cos (t) dt = C - 3*t*cos (t) - 3*t*sin (t) - 3*sin (t)*cos(t) + 3*cos (t)*sin(t) + 8*cos (t)*sin (t) - 9*t*cos (t)*sin (t) - 9*t*cos (t)*sin (t) | /
$$\int - 48 \sin^{4}{\left(t \right)} \cos^{2}{\left(t \right)}\, dt = C - 3 t \sin^{6}{\left(t \right)} - 9 t \sin^{4}{\left(t \right)} \cos^{2}{\left(t \right)} - 9 t \sin^{2}{\left(t \right)} \cos^{4}{\left(t \right)} - 3 t \cos^{6}{\left(t \right)} - 3 \sin^{5}{\left(t \right)} \cos{\left(t \right)} + 8 \sin^{3}{\left(t \right)} \cos^{3}{\left(t \right)} + 3 \sin{\left(t \right)} \cos^{5}{\left(t \right)}$$
Gráfica
Respuesta
[src]
___
3*\/ 3
pi + -------
4
$$\frac{3 \sqrt{3}}{4} + \pi$$
=
=
___
3*\/ 3
pi + -------
4
$$\frac{3 \sqrt{3}}{4} + \pi$$
pi + 3*sqrt(3)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.