Sr Examen
Integral de sqrt((2sin2x-2sinx)^2+(2cosx-2cos2x)^2) dx
Solución
Ha introducido
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pi / | | _____________________________________________________ | / 2 2 | \/ (2*sin(2*x) - 2*sin(x)) + (2*cos(x) - 2*cos(2*x)) dx | / 0
$$\int\limits_{0}^{\pi} \sqrt{\left(- 2 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right)^{2} + \left(2 \cos{\left(x \right)} - 2 \cos{\left(2 x \right)}\right)^{2}}\, dx$$
Integral(sqrt((2*sin(2*x) - 2*sin(x))^2 + (2*cos(x) - 2*cos(2*x))^2), (x, 0, pi))
Respuesta (Indefinida)
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/ / | | | _____________________________________________________ | ___________________________________________________________________________________ | / 2 2 | / 2 2 2 2 | \/ (2*sin(2*x) - 2*sin(x)) + (2*cos(x) - 2*cos(2*x)) dx = C + 2* | \/ cos (x) + cos (2*x) + sin (x) + sin (2*x) - 2*cos(x)*cos(2*x) - 2*sin(x)*sin(2*x) dx | | / /
$$\int \sqrt{\left(- 2 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right)^{2} + \left(2 \cos{\left(x \right)} - 2 \cos{\left(2 x \right)}\right)^{2}}\, dx = C + 2 \int \sqrt{\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} \sin{\left(2 x \right)} + \sin^{2}{\left(2 x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} \cos{\left(2 x \right)} + \cos^{2}{\left(2 x \right)}}\, dx$$
Respuesta
[src]
pi
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2* | \/ cos (x) + cos (2*x) + sin (x) + sin (2*x) - 2*cos(x)*cos(2*x) - 2*sin(x)*sin(2*x) dx
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0
$$2 \int\limits_{0}^{\pi} \sqrt{\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} \sin{\left(2 x \right)} + \sin^{2}{\left(2 x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} \cos{\left(2 x \right)} + \cos^{2}{\left(2 x \right)}}\, dx$$
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pi
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2* | \/ cos (x) + cos (2*x) + sin (x) + sin (2*x) - 2*cos(x)*cos(2*x) - 2*sin(x)*sin(2*x) dx
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0
$$2 \int\limits_{0}^{\pi} \sqrt{\sin^{2}{\left(x \right)} - 2 \sin{\left(x \right)} \sin{\left(2 x \right)} + \sin^{2}{\left(2 x \right)} + \cos^{2}{\left(x \right)} - 2 \cos{\left(x \right)} \cos{\left(2 x \right)} + \cos^{2}{\left(2 x \right)}}\, dx$$
2*Integral(sqrt(cos(x)^2 + cos(2*x)^2 + sin(x)^2 + sin(2*x)^2 - 2*cos(x)*cos(2*x) - 2*sin(x)*sin(2*x)), (x, 0, pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.