Sr Examen
Integral de sqrt(sinx)/(sqrt(sinx)+sqrt(cosx))1/sinx dx
Solución
Ha introducido
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1 / | | / ________ \ | | \/ sin(x) | | |-----------------------| | | ________ ________| | \\/ sin(x) + \/ cos(x) / | ------------------------- dx | sin(x) | / 0
$$\int\limits_{0}^{1} \frac{\frac{1}{\sqrt{\sin{\left(x \right)}} + \sqrt{\cos{\left(x \right)}}} \sqrt{\sin{\left(x \right)}}}{\sin{\left(x \right)}}\, dx$$
Integral((sqrt(sin(x))/(sqrt(sin(x)) + sqrt(cos(x))))/sin(x), (x, 0, 1))
Respuesta (Indefinida)
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/
|
| / ________ \
| | \/ sin(x) |
| |-----------------------| /
| | ________ ________| |
| \\/ sin(x) + \/ cos(x) / | 1
| ------------------------- dx = C + | ------------------------------------ dx
| sin(x) | / ________ ________\ ________
| | \\/ cos(x) + \/ sin(x) /*\/ sin(x)
/ |
/
$$\int \frac{\frac{1}{\sqrt{\sin{\left(x \right)}} + \sqrt{\cos{\left(x \right)}}} \sqrt{\sin{\left(x \right)}}}{\sin{\left(x \right)}}\, dx = C + \int \frac{1}{\left(\sqrt{\sin{\left(x \right)}} + \sqrt{\cos{\left(x \right)}}\right) \sqrt{\sin{\left(x \right)}}}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.