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