Sr Examen
Integral de xcos(2x)^2 dx
Solución
Ha introducido
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1 / | | 2 | x*cos (2*x) dx | / 0
$$\int\limits_{0}^{1} x \cos^{2}{\left(2 x \right)}\, dx$$
Integral(x*cos(2*x)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ | 2 2 2 2 2 | 2 cos (2*x) x *cos (2*x) x *sin (2*x) x*cos(2*x)*sin(2*x) | x*cos (2*x) dx = C + --------- + ------------ + ------------ + ------------------- | 16 4 4 4 /
$$\int x \cos^{2}{\left(2 x \right)}\, dx = C + \frac{x^{2} \sin^{2}{\left(2 x \right)}}{4} + \frac{x^{2} \cos^{2}{\left(2 x \right)}}{4} + \frac{x \sin{\left(2 x \right)} \cos{\left(2 x \right)}}{4} + \frac{\cos^{2}{\left(2 x \right)}}{16}$$
Gráfica
Respuesta
[src]
2 2 cos (2) 3*sin (2) cos(2)*sin(2) ------- + --------- + ------------- 4 16 4
$$\frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{4} + \frac{\cos^{2}{\left(2 \right)}}{4} + \frac{3 \sin^{2}{\left(2 \right)}}{16}$$
=
=
2 2 cos (2) 3*sin (2) cos(2)*sin(2) ------- + --------- + ------------- 4 16 4
$$\frac{\sin{\left(2 \right)} \cos{\left(2 \right)}}{4} + \frac{\cos^{2}{\left(2 \right)}}{4} + \frac{3 \sin^{2}{\left(2 \right)}}{16}$$
cos(2)^2/4 + 3*sin(2)^2/16 + cos(2)*sin(2)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.