Sr Examen
Integral de sqrt(1+(cos((pi*x)/2)/sin((pi*x)/2))^2) dx
Solución
Ha introducido
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3/2 / | | __________________ | / 2 | / / /pi*x\\ | / |cos|----|| | / | \ 2 /| | / 1 + |---------| dx | / | /pi*x\| | / |sin|----|| | \/ \ \ 2 // | / 1
$$\int\limits_{1}^{\frac{3}{2}} \sqrt{\left(\frac{\cos{\left(\frac{\pi x}{2} \right)}}{\sin{\left(\frac{\pi x}{2} \right)}}\right)^{2} + 1}\, dx$$
Integral(sqrt(1 + (cos((pi*x)/2)/sin((pi*x)/2))^2), (x, 1, 3/2))
Respuesta
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3/2 / | | _________________________ | / 2/pi*x\ 2/pi*x\ | / cos |----| + sin |----| | \/ \ 2 / \ 2 / | ----------------------------- dx | | /pi*x\| | |sin|----|| | | \ 2 /| | / 1
$$\int\limits_{1}^{\frac{3}{2}} \frac{\sqrt{\sin^{2}{\left(\frac{\pi x}{2} \right)} + \cos^{2}{\left(\frac{\pi x}{2} \right)}}}{\left|{\sin{\left(\frac{\pi x}{2} \right)}}\right|}\, dx$$
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3/2 / | | _________________________ | / 2/pi*x\ 2/pi*x\ | / cos |----| + sin |----| | \/ \ 2 / \ 2 / | ----------------------------- dx | | /pi*x\| | |sin|----|| | | \ 2 /| | / 1
$$\int\limits_{1}^{\frac{3}{2}} \frac{\sqrt{\sin^{2}{\left(\frac{\pi x}{2} \right)} + \cos^{2}{\left(\frac{\pi x}{2} \right)}}}{\left|{\sin{\left(\frac{\pi x}{2} \right)}}\right|}\, dx$$
Integral(sqrt(cos(pi*x/2)^2 + sin(pi*x/2)^2)/Abs(sin(pi*x/2)), (x, 1, 3/2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.