Question

integrala de la 0 la infinit din e^-5x dx cat este?

Answer 1

$\int\limits^\infty_ 0{e^{-5x}} dx = - \frac{1}{5} \int\limits^\infty_ 0{(-5x)'\cdot e^{-5x}} = - \frac{1}{5}\cdot e^{-5x} \big|_0^\infty = \\ \\= - \frac{1}{5}\cdot e^{-5\cdot \infty} + \frac{1}{5}\cdot e^{-5\cdot 0} = - \frac{1}{5}\cdot \frac{1}{e^{5\cdot \infty}} + \frac{1}{5}\cdot 1 =\frac{1}{5}\cdot 0 + \frac{1}{5} = \frac{1}{5}$