Sr Examen
Resolución de integrales/
|1+a^2*cos(2x)^2+(1-a)^2*cos(x)^2-2a*cos(2x)-2(1-a)*cos(x)+2a(1-a)cos(2x)cos(x)|
Integral de |1+a^2*cos(2x)^2+(1-a)^2*cos(x)^2-2a*cos(2x)-2(1-a)*cos(x)+2a(1-a)cos(2x)cos(x)| dx
Solución
Ha introducido
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pi / | | | 2 2 2 2 | | |1 + a *cos (2*x) + (1 - a) *cos (x) - 2*a*cos(2*x) - 2*(1 - a)*cos(x) + 2*a*(1 - a)*cos(2*x)*cos(x)| dx | / -pi
$$\int\limits_{- \pi}^{\pi} \left|{2 a \left(1 - a\right) \cos{\left(2 x \right)} \cos{\left(x \right)} + \left(- 2 \left(1 - a\right) \cos{\left(x \right)} + \left(- 2 a \cos{\left(2 x \right)} + \left(\left(1 - a\right)^{2} \cos^{2}{\left(x \right)} + \left(a^{2} \cos^{2}{\left(2 x \right)} + 1\right)\right)\right)\right)}\right|\, dx$$
Integral(Abs(1 + a^2*cos(2*x)^2 + (1 - a)^2*cos(x)^2 - 2*a*cos(2*x) - 2*(1 - a)*cos(x) + (((2*a)*(1 - a))*cos(2*x))*cos(x)), (x, -pi, pi))
Respuesta
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pi / | | | 2 2 2 2 | | |1 + a *cos (2*x) + (1 - a) *cos (x) - 2*a*cos(2*x) - 2*(1 - a)*cos(x) + 2*a*(1 - a)*cos(x)*cos(2*x)| dx | / -pi
$$\int\limits_{- \pi}^{\pi} \left|{a^{2} \cos^{2}{\left(2 x \right)} + 2 a \left(1 - a\right) \cos{\left(x \right)} \cos{\left(2 x \right)} - 2 a \cos{\left(2 x \right)} + \left(1 - a\right)^{2} \cos^{2}{\left(x \right)} - 2 \left(1 - a\right) \cos{\left(x \right)} + 1}\right|\, dx$$
=
=
pi / | | | 2 2 2 2 | | |1 + a *cos (2*x) + (1 - a) *cos (x) - 2*a*cos(2*x) - 2*(1 - a)*cos(x) + 2*a*(1 - a)*cos(x)*cos(2*x)| dx | / -pi
$$\int\limits_{- \pi}^{\pi} \left|{a^{2} \cos^{2}{\left(2 x \right)} + 2 a \left(1 - a\right) \cos{\left(x \right)} \cos{\left(2 x \right)} - 2 a \cos{\left(2 x \right)} + \left(1 - a\right)^{2} \cos^{2}{\left(x \right)} - 2 \left(1 - a\right) \cos{\left(x \right)} + 1}\right|\, dx$$
Integral(Abs(1 + a^2*cos(2*x)^2 + (1 - a)^2*cos(x)^2 - 2*a*cos(2*x) - 2*(1 - a)*cos(x) + 2*a*(1 - a)*cos(x)*cos(2*x)), (x, -pi, pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.