Sr Examen
Integral de √((-2sint+2sin2t)^2+(2cost-2cos2t)^2) dx
Solución
Ha introducido
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pi / | | ______________________________________________________ | / 2 2 | \/ (-2*sin(t) + 2*sin(2*t)) + (2*cos(t) - 2*cos(2*t)) dt | / 0
$$\int\limits_{0}^{\pi} \sqrt{\left(- 2 \sin{\left(t \right)} + 2 \sin{\left(2 t \right)}\right)^{2} + \left(2 \cos{\left(t \right)} - 2 \cos{\left(2 t \right)}\right)^{2}}\, dt$$
Integral(sqrt((-2*sin(t) + 2*sin(2*t))^2 + (2*cos(t) - 2*cos(2*t))^2), (t, 0, pi))
Respuesta (Indefinida)
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/ / | | | ______________________________________________________ | ___________________________________________________________________________________ | / 2 2 | / 2 2 2 2 | \/ (-2*sin(t) + 2*sin(2*t)) + (2*cos(t) - 2*cos(2*t)) dt = C + 2* | \/ cos (t) + cos (2*t) + sin (t) + sin (2*t) - 2*cos(t)*cos(2*t) - 2*sin(t)*sin(2*t) dt | | / /
$$\int \sqrt{\left(- 2 \sin{\left(t \right)} + 2 \sin{\left(2 t \right)}\right)^{2} + \left(2 \cos{\left(t \right)} - 2 \cos{\left(2 t \right)}\right)^{2}}\, dt = C + 2 \int \sqrt{\sin^{2}{\left(t \right)} - 2 \sin{\left(t \right)} \sin{\left(2 t \right)} + \sin^{2}{\left(2 t \right)} + \cos^{2}{\left(t \right)} - 2 \cos{\left(t \right)} \cos{\left(2 t \right)} + \cos^{2}{\left(2 t \right)}}\, dt$$
Respuesta
[src]
pi
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2* | \/ cos (t) + cos (2*t) + sin (t) + sin (2*t) - 2*cos(t)*cos(2*t) - 2*sin(t)*sin(2*t) dt
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0
$$2 \int\limits_{0}^{\pi} \sqrt{\sin^{2}{\left(t \right)} - 2 \sin{\left(t \right)} \sin{\left(2 t \right)} + \sin^{2}{\left(2 t \right)} + \cos^{2}{\left(t \right)} - 2 \cos{\left(t \right)} \cos{\left(2 t \right)} + \cos^{2}{\left(2 t \right)}}\, dt$$
=
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pi
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2* | \/ cos (t) + cos (2*t) + sin (t) + sin (2*t) - 2*cos(t)*cos(2*t) - 2*sin(t)*sin(2*t) dt
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0
$$2 \int\limits_{0}^{\pi} \sqrt{\sin^{2}{\left(t \right)} - 2 \sin{\left(t \right)} \sin{\left(2 t \right)} + \sin^{2}{\left(2 t \right)} + \cos^{2}{\left(t \right)} - 2 \cos{\left(t \right)} \cos{\left(2 t \right)} + \cos^{2}{\left(2 t \right)}}\, dt$$
2*Integral(sqrt(cos(t)^2 + cos(2*t)^2 + sin(t)^2 + sin(2*t)^2 - 2*cos(t)*cos(2*t) - 2*sin(t)*sin(2*t)), (t, 0, pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.