Question
$$f ( t ) = \left\{ \begin{array} { l l } { e ^ { 2 t } , } & { 0 < t < 3 } \\ { 1 , } & { 3 < t } \end{array} \right.$$
Step 1
The Laplace transform is defined as: $$L\{f(t)\}=\int_0^\infty e^{-st}f(t)dt$$ So we have: $$L\{f(t)\}=\int_0^3 e^{-st}e^{2t}dt + \int_3^\infty e^{-st}dt$$ Show more…
Show all steps
Your feedback will help us improve your experience
Jacob Denson and 83 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
$$f ( t ) = \left\{ \begin{array} { l l } { 0 , } & { 0 < t < 2 } \\ { t , } & { 2 < t } \end{array} \right.$$
Laplace Transforms
Definition of the Laplace Transform
$$f ( t ) = \left\{ \begin{array} { l l } { 1 - t , } & { 0 < t < 1 } \\ { 0 , } & { 1 < t } \end{array} \right.$$
$g(t)=\left\{\begin{array}{ll}{0,} & {0< t <1} \\ {2,} & {1< t <2} \\ {1,} & {2 < t < 3} \\ {3,} & {3 < t}\end{array}\right.$
Transforms of Discontinuous Functions
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD