Sr Examen
Integral de cos(x)^2*x^3 dx
Solución
Ha introducido
[src]
2 / | | 2 3 | cos (x)*x dx | / 0
$$\int\limits_{0}^{2} x^{3} \cos^{2}{\left(x \right)}\, dx$$
Integral(cos(x)^2*x^3, (x, 0, 2))
Respuesta (Indefinida)
[src]
/ | 2 2 2 4 2 4 2 2 2 3 | 2 3 3*sin (x) 3*x *sin (x) x *cos (x) x *sin (x) 3*x *cos (x) x *cos(x)*sin(x) 3*x*cos(x)*sin(x) | cos (x)*x dx = C + --------- - ------------ + ---------- + ---------- + ------------ + ---------------- - ----------------- | 8 8 8 8 8 2 4 /
$$\int x^{3} \cos^{2}{\left(x \right)}\, dx = C + \frac{x^{4} \sin^{2}{\left(x \right)}}{8} + \frac{x^{4} \cos^{2}{\left(x \right)}}{8} + \frac{x^{3} \sin{\left(x \right)} \cos{\left(x \right)}}{2} - \frac{3 x^{2} \sin^{2}{\left(x \right)}}{8} + \frac{3 x^{2} \cos^{2}{\left(x \right)}}{8} - \frac{3 x \sin{\left(x \right)} \cos{\left(x \right)}}{4} + \frac{3 \sin^{2}{\left(x \right)}}{8}$$
Gráfica
Respuesta
[src]
2 2
7*cos (2) 7*sin (2) 5*cos(2)*sin(2)
--------- + --------- + ---------------
2 8 2
$$\frac{5 \sin{\left(2 \right)} \cos{\left(2 \right)}}{2} + \frac{7 \cos^{2}{\left(2 \right)}}{2} + \frac{7 \sin^{2}{\left(2 \right)}}{8}$$
=
=
2 2
7*cos (2) 7*sin (2) 5*cos(2)*sin(2)
--------- + --------- + ---------------
2 8 2
$$\frac{5 \sin{\left(2 \right)} \cos{\left(2 \right)}}{2} + \frac{7 \cos^{2}{\left(2 \right)}}{2} + \frac{7 \sin^{2}{\left(2 \right)}}{8}$$
7*cos(2)^2/2 + 7*sin(2)^2/8 + 5*cos(2)*sin(2)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.