Sr Examen
Integral de sqrt(1+(-cos(x)/sin(x))^2) dx
Solución
Ha introducido
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pi -- 4 / | | _________________ | / 2 | / /-cos(x) \ | / 1 + |--------| dx | \/ \ sin(x) / | / pi -- 2
$$\int\limits_{\frac{\pi}{2}}^{\frac{\pi}{4}} \sqrt{\left(\frac{\left(-1\right) \cos{\left(x \right)}}{\sin{\left(x \right)}}\right)^{2} + 1}\, dx$$
Integral(sqrt(1 + ((-cos(x))/sin(x))^2), (x, pi/2, pi/4))
Respuesta
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pi -- 4 / | | ___________________ | / 2 2 | \/ cos (x) + sin (x) | ---------------------- dx | |sin(x)| | / pi -- 2
$$\int\limits_{\frac{\pi}{2}}^{\frac{\pi}{4}} \frac{\sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}}{\left|{\sin{\left(x \right)}}\right|}\, dx$$
=
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pi -- 4 / | | ___________________ | / 2 2 | \/ cos (x) + sin (x) | ---------------------- dx | |sin(x)| | / pi -- 2
$$\int\limits_{\frac{\pi}{2}}^{\frac{\pi}{4}} \frac{\sqrt{\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}}}{\left|{\sin{\left(x \right)}}\right|}\, dx$$
Integral(sqrt(cos(x)^2 + sin(x)^2)/Abs(sin(x)), (x, pi/2, pi/4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.