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