Sr Examen
Integral de sin(x)/((abs(1-x^2))^0.5) dx
Solución
Ha introducido
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6/5 / | | sin(x) | ------------- dx | __________ | / | 2| | \/ |1 - x | | / 1/2
$$\int\limits_{\frac{1}{2}}^{\frac{6}{5}} \frac{\sin{\left(x \right)}}{\sqrt{\left|{1 - x^{2}}\right|}}\, dx$$
Integral(sin(x)/sqrt(|1 - x^2|), (x, 1/2, 6/5))
Respuesta (Indefinida)
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/ / | | | sin(x) | sin(x) | ------------- dx = C + | ------------- dx | __________ | __________ | / | 2| | / | 2| | \/ |1 - x | | \/ |1 - x | | | / /
$$\int \frac{\sin{\left(x \right)}}{\sqrt{\left|{1 - x^{2}}\right|}}\, dx = C + \int \frac{\sin{\left(x \right)}}{\sqrt{\left|{1 - x^{2}}\right|}}\, dx$$
Respuesta
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6/5 / | | / sin(x) 2 | |-------------------- for -1 + x >= 0 | | _______ ________ | |\/ 1 + x *\/ -1 + x | < dx | | sin(x) | |------------------- otherwise | | _______ _______ | \\/ 1 + x *\/ 1 - x | / 1/2
$$\int\limits_{\frac{1}{2}}^{\frac{6}{5}} \begin{cases} \frac{\sin{\left(x \right)}}{\sqrt{x - 1} \sqrt{x + 1}} & \text{for}\: x^{2} - 1 \geq 0 \\\frac{\sin{\left(x \right)}}{\sqrt{1 - x} \sqrt{x + 1}} & \text{otherwise} \end{cases}\, dx$$
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6/5 / | | / sin(x) 2 | |-------------------- for -1 + x >= 0 | | _______ ________ | |\/ 1 + x *\/ -1 + x | < dx | | sin(x) | |------------------- otherwise | | _______ _______ | \\/ 1 + x *\/ 1 - x | / 1/2
$$\int\limits_{\frac{1}{2}}^{\frac{6}{5}} \begin{cases} \frac{\sin{\left(x \right)}}{\sqrt{x - 1} \sqrt{x + 1}} & \text{for}\: x^{2} - 1 \geq 0 \\\frac{\sin{\left(x \right)}}{\sqrt{1 - x} \sqrt{x + 1}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((sin(x)/(sqrt(1 + x)*sqrt(-1 + x)), -1 + x^2 >= 0), (sin(x)/(sqrt(1 + x)*sqrt(1 - x)), True)), (x, 1/2, 6/5))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.