Sr Examen
Integral de (sin(x)/e^x)^2 dx
Solución
Ha introducido
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1 / | | 2 | /sin(x)\ | |------| dx | | x | | \ E / | / 0
$$\int\limits_{0}^{1} \left(\frac{\sin{\left(x \right)}}{e^{x}}\right)^{2}\, dx$$
Integral((sin(x)/E^x)^2, (x, 0, 1))
Respuesta (Indefinida)
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/ | | 2 2 -2*x 2 -2*x -2*x | /sin(x)\ 3*sin (x)*e cos (x)*e cos(x)*e *sin(x) | |------| dx = C - --------------- - ------------- - ------------------- | | x | 8 8 4 | \ E / | /
$$\int \left(\frac{\sin{\left(x \right)}}{e^{x}}\right)^{2}\, dx = C - \frac{3 e^{- 2 x} \sin^{2}{\left(x \right)}}{8} - \frac{e^{- 2 x} \sin{\left(x \right)} \cos{\left(x \right)}}{4} - \frac{e^{- 2 x} \cos^{2}{\left(x \right)}}{8}$$
Gráfica
Respuesta
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2 -2 2 -2 -2 1 3*sin (1)*e cos (1)*e cos(1)*e *sin(1) - - ------------- - ----------- - ----------------- 8 8 8 4
$$- \frac{3 \sin^{2}{\left(1 \right)}}{8 e^{2}} - \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{4 e^{2}} - \frac{\cos^{2}{\left(1 \right)}}{8 e^{2}} + \frac{1}{8}$$
=
=
2 -2 2 -2 -2 1 3*sin (1)*e cos (1)*e cos(1)*e *sin(1) - - ------------- - ----------- - ----------------- 8 8 8 4
$$- \frac{3 \sin^{2}{\left(1 \right)}}{8 e^{2}} - \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{4 e^{2}} - \frac{\cos^{2}{\left(1 \right)}}{8 e^{2}} + \frac{1}{8}$$
1/8 - 3*sin(1)^2*exp(-2)/8 - cos(1)^2*exp(-2)/8 - cos(1)*exp(-2)*sin(1)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.