Sr Examen
Integral de sqrt(((3(1-cos(f)))^2+(3(sin(f)))^2)) df
Solución
Ha introducido
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pi / | | _________________________________ | / 2 2 | \/ (3*(1 - cos(f))) + (3*sin(f)) df | / 0
$$\int\limits_{0}^{\pi} \sqrt{\left(3 \left(1 - \cos{\left(f \right)}\right)\right)^{2} + \left(3 \sin{\left(f \right)}\right)^{2}}\, df$$
Integral(sqrt((3*(1 - cos(f)))^2 + (3*sin(f))^2), (f, 0, pi))
Respuesta (Indefinida)
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/ / | | | _________________________________ | __________________________________ | / 2 2 | / 2 2 | \/ (3*(1 - cos(f))) + (3*sin(f)) df = C + 3* | \/ 1 + cos (f) + sin (f) - 2*cos(f) df | | / /
$$\int \sqrt{\left(3 \left(1 - \cos{\left(f \right)}\right)\right)^{2} + \left(3 \sin{\left(f \right)}\right)^{2}}\, df = C + 3 \int \sqrt{\sin^{2}{\left(f \right)} + \cos^{2}{\left(f \right)} - 2 \cos{\left(f \right)} + 1}\, df$$
Respuesta
[src]
pi
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3* | \/ 1 + cos (f) + sin (f) - 2*cos(f) df
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0
$$3 \int\limits_{0}^{\pi} \sqrt{\sin^{2}{\left(f \right)} + \cos^{2}{\left(f \right)} - 2 \cos{\left(f \right)} + 1}\, df$$
=
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pi
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3* | \/ 1 + cos (f) + sin (f) - 2*cos(f) df
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0
$$3 \int\limits_{0}^{\pi} \sqrt{\sin^{2}{\left(f \right)} + \cos^{2}{\left(f \right)} - 2 \cos{\left(f \right)} + 1}\, df$$
3*Integral(sqrt(1 + cos(f)^2 + sin(f)^2 - 2*cos(f)), (f, 0, pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.