Sr Examen
Integral de 24cos^2(t)sin^4(t) dt
Solución
Ha introducido
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pi -- 2 / | | 2 4 | 24*cos (t)*sin (t) dt | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} \sin^{4}{\left(t \right)} 24 \cos^{2}{\left(t \right)}\, dt$$
Integral((24*cos(t)^2)*sin(t)^4, (t, 0, pi/2))
Respuesta (Indefinida)
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/ | 5 6 6 5 2 4 4 2 | 2 4 3 3 3*cos (t)*sin(t) 3*t*cos (t) 3*t*sin (t) 3*sin (t)*cos(t) 9*t*cos (t)*sin (t) 9*t*cos (t)*sin (t) | 24*cos (t)*sin (t) dt = C - 4*cos (t)*sin (t) - ---------------- + ----------- + ----------- + ---------------- + ------------------- + ------------------- | 2 2 2 2 2 2 /
$$\int \sin^{4}{\left(t \right)} 24 \cos^{2}{\left(t \right)}\, dt = C + \frac{3 t \sin^{6}{\left(t \right)}}{2} + \frac{9 t \sin^{4}{\left(t \right)} \cos^{2}{\left(t \right)}}{2} + \frac{9 t \sin^{2}{\left(t \right)} \cos^{4}{\left(t \right)}}{2} + \frac{3 t \cos^{6}{\left(t \right)}}{2} + \frac{3 \sin^{5}{\left(t \right)} \cos{\left(t \right)}}{2} - 4 \sin^{3}{\left(t \right)} \cos^{3}{\left(t \right)} - \frac{3 \sin{\left(t \right)} \cos^{5}{\left(t \right)}}{2}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.