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