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