Sr Examen
Integral de sqtr((2+2*cos(x))^2+(-2*sin(x))^2) dx
Solución
Ha introducido
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pi / | | ________________________________ | / 2 2 | \/ (2 + 2*cos(x)) + (-2*sin(x)) dx | / 0
$$\int\limits_{0}^{\pi} \sqrt{\left(2 \cos{\left(x \right)} + 2\right)^{2} + \left(- 2 \sin{\left(x \right)}\right)^{2}}\, dx$$
Integral(sqrt((2 + 2*cos(x))^2 + (-2*sin(x))^2), (x, 0, pi))
Respuesta (Indefinida)
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/ / | | | ________________________________ | __________________________________ | / 2 2 | / 2 2 | \/ (2 + 2*cos(x)) + (-2*sin(x)) dx = C + 2* | \/ 1 + cos (x) + sin (x) + 2*cos(x) dx | | / /
$$\int \sqrt{\left(2 \cos{\left(x \right)} + 2\right)^{2} + \left(- 2 \sin{\left(x \right)}\right)^{2}}\, dx = C + 2 \int \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} + 2 \cos{\left(x \right)} + 1}\, dx$$
Respuesta
[src]
pi
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2* | \/ 1 + cos (x) + sin (x) + 2*cos(x) dx
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0
$$2 \int\limits_{0}^{\pi} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} + 2 \cos{\left(x \right)} + 1}\, dx$$
=
=
pi
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| / 2 2
2* | \/ 1 + cos (x) + sin (x) + 2*cos(x) dx
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/
0
$$2 \int\limits_{0}^{\pi} \sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)} + 2 \cos{\left(x \right)} + 1}\, dx$$
2*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.