Find 10 [ u ( t − 2 ) − u ( t − 3 ) ] ⏞ x ( t ) ∗ e − t u ( t ) ⏞ h ( t ) {\displaystyle \overbrace {10[u(t-2)-u(t-3)]} ^{x(t)}*\overbrace {e^{-t}u(t)} ^{h(t)}}
10 [ u ( t − 2 ) − u ( t − 3 ) ] ∗ e − t u ( t ) = { 0 , t ≤ 2 ∫ t − 3 t − 2 10 ⋅ e − λ d λ , t > 2 = { 0 , t ≤ 2 10 e 3 − t − 10 e 2 − t , t > 2 {\displaystyle 10[u(t-2)-u(t-3)]*e^{-t}u(t)={\begin{cases}0,&t\leq 2\\\int _{t-3}^{t-2}10\cdot e^{-\lambda }\,d\lambda ,&t>2\\\end{cases}}={\begin{cases}0,&t\leq 2\\10\,e^{3-t}-10\,e^{2-t},&t>2\\\end{cases}}}
![{\displaystyle \overbrace {10[u(t-2)-u(t-3)]} ^{x(t)}*\overbrace {e^{-t}u(t)} ^{h(t)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/138aa913f26a9ea9e91bac08f8a2ac3df40a3e34)
![{\displaystyle 10[u(t-2)-u(t-3)]*e^{-t}u(t)={\begin{cases}0,&t\leq 2\\\int _{t-3}^{t-2}10\cdot e^{-\lambda }\,d\lambda ,&t>2\\\end{cases}}={\begin{cases}0,&t\leq 2\\10\,e^{3-t}-10\,e^{2-t},&t>2\\\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b415c7531b6397061ff2aed57ee27f4e72779c95)
