Sr Examen
Integral de x^2*cos^4(x) dx
Solución
Ha introducido
[src]
pi -- 2 / | | 2 4 | x *cos (x) dx | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} x^{2} \cos^{4}{\left(x \right)}\, dx$$
Integral(x^2*cos(x)^4, (x, 0, pi/2))
Respuesta (Indefinida)
[src]
/ | 3 4 3 3 4 3 4 4 2 2 3 2 2 2 3 2 3 | 2 4 17*cos (x)*sin(x) 15*x*sin (x) 15*sin (x)*cos(x) x *cos (x) x *sin (x) 17*x*cos (x) 3*x*cos (x)*sin (x) x *cos (x)*sin (x) 3*x *sin (x)*cos(x) 5*x *cos (x)*sin(x) | x *cos (x) dx = C - ----------------- - ------------ - ----------------- + ---------- + ---------- + ------------ - ------------------- + ------------------ + ------------------- + ------------------- | 64 64 64 8 8 64 32 4 8 8 /
$$\int x^{2} \cos^{4}{\left(x \right)}\, dx = C + \frac{x^{3} \sin^{4}{\left(x \right)}}{8} + \frac{x^{3} \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{x^{3} \cos^{4}{\left(x \right)}}{8} + \frac{3 x^{2} \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} + \frac{5 x^{2} \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8} - \frac{15 x \sin^{4}{\left(x \right)}}{64} - \frac{3 x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{32} + \frac{17 x \cos^{4}{\left(x \right)}}{64} - \frac{15 \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{64} - \frac{17 \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{64}$$
Gráfica
Respuesta
[src]
3 15*pi pi - ----- + --- 128 64
$$- \frac{15 \pi}{128} + \frac{\pi^{3}}{64}$$
=
=
3 15*pi pi - ----- + --- 128 64
$$- \frac{15 \pi}{128} + \frac{\pi^{3}}{64}$$
-15*pi/128 + pi^3/64
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.