Impulse response of a continuous time system
\begin{align}
y(2.34) &amp;= h \star x\,\big\vert_{t=2.34}\\
&amp;= \int_{-\infty}^\infty h(\tau)x(2.34-\tau)\,\mathrm d\tau
&amp;\scriptstyle{\text{from the definition of the convolution integral}} \\
&amp;= \int_0^\infty e^{-\tau}x(2.34-\tau)\,\mathrm d\tau &amp;\scriptstyle{\text{because } h(\tau)=0\text{ for }\tau &lt; 0}\\
&amp;= \int_0^\infty e^{-\tau}u(1.34-\tau)\,\mathrm d\tau &amp;\scriptstyle{\text{because }x(2.34-\tau) = u((2.34-\tau)-1)}\\
&amp;= \int_0^{1.34} e^{-\tau}\,\mathrm d\tau
&amp;\scriptstyle{\text{because }u(1.34-\tau) = 0 \text{ for }\tau &lt; 1.34}\\
&amp;= 1-e^{-1.34}
\end{align}