Sr Examen
Integral de abs(x*x+2*x-3)^-(0.5) dx
Solución
Ha introducido
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21 -- 10 / | | 1 | ------------------- dx | _________________ | \/ |x*x + 2*x - 3| | / 0
$$\int\limits_{0}^{\frac{21}{10}} \frac{1}{\sqrt{\left|{\left(x x + 2 x\right) - 3}\right|}}\, dx$$
Integral(1/sqrt(|x*x + 2*x - 3|), (x, 0, 21/10))
Respuesta
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21 -- 10 / | | / 1 2 | |-------------------- for -3 + x + 2*x >= 0 | | ________ _______ | |\/ -1 + x *\/ 3 + x | < dx | | 1 | |------------------- otherwise | | _______ _______ | \\/ 1 - x *\/ 3 + x | / 0
$$\int\limits_{0}^{\frac{21}{10}} \begin{cases} \frac{1}{\sqrt{x - 1} \sqrt{x + 3}} & \text{for}\: x^{2} + 2 x - 3 \geq 0 \\\frac{1}{\sqrt{1 - x} \sqrt{x + 3}} & \text{otherwise} \end{cases}\, dx$$
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21 -- 10 / | | / 1 2 | |-------------------- for -3 + x + 2*x >= 0 | | ________ _______ | |\/ -1 + x *\/ 3 + x | < dx | | 1 | |------------------- otherwise | | _______ _______ | \\/ 1 - x *\/ 3 + x | / 0
$$\int\limits_{0}^{\frac{21}{10}} \begin{cases} \frac{1}{\sqrt{x - 1} \sqrt{x + 3}} & \text{for}\: x^{2} + 2 x - 3 \geq 0 \\\frac{1}{\sqrt{1 - x} \sqrt{x + 3}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((1/(sqrt(-1 + x)*sqrt(3 + x)), -3 + x^2 + 2*x >= 0), (1/(sqrt(1 - x)*sqrt(3 + x)), True)), (x, 0, 21/10))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.