- #1
karush
Gold Member
MHB
- 3,269
- 5
$\tiny\text{Leeward 206 {8.13} Integral at infinity}$
$$I=\int_{0} ^{\infty} e^{-ax} \,dx \ a>0 =
\\
\begin{align}\displaystyle
u& = -ax &
du&=-a \ d{x}
\end{align} \\
\text{then} \\
I=-\frac{1}{a}\int_{0} ^{\infty} e^{x} \,dx
=-\dfrac{\mathrm{e}^{-ax}}{a}+C \\
\text{hopefully, wasn't sure about the + C}$$
$\tiny\text{ Surf the Nations math study group}$
$$I=\int_{0} ^{\infty} e^{-ax} \,dx \ a>0 =
\\
\begin{align}\displaystyle
u& = -ax &
du&=-a \ d{x}
\end{align} \\
\text{then} \\
I=-\frac{1}{a}\int_{0} ^{\infty} e^{x} \,dx
=-\dfrac{\mathrm{e}^{-ax}}{a}+C \\
\text{hopefully, wasn't sure about the + C}$$
$\tiny\text{ Surf the Nations math study group}$