(5.1) Calculate the Laplace transform of the following function from first principles: \(f(t) = \begin{cases} 4, & 0 \le t < 1 \\ 0, & t \ge 1 \end{cases}\)
Added by Paula M.
Close
Step 1
Therefore, we can split the integral into two parts: $$F(s) = \int_0^1 e^{-st} (4) dt + \int_1^\infty e^{-st} (0) dt$$ Show more…
Show all steps
Your feedback will help us improve your experience
Bhushan Arora and 89 other Calculus 1 / AB 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
Calculate the Laplace transform of the following function: f(t) = { 0 if 0 < t < 1, e^t if 1 < t
Bhushan A.
Write each function in terms of unit step functions. Find the Laplace transform of the given function. $$f(t)=\left\{\begin{array}{lr} 1, & 0 \leq t<4 \\ 0, & 4 \leq t<5 \\ 1, & t \geq 5 \end{array}\right.$$
The Laplace Transform
Operational Properties I
Find the Laplace transform of the given function. $$ f(t)=\left\{\begin{array}{ll}{0,} & {t<1} \\ {t^{2}-2 t+2,} & {t \geq 1}\end{array}\right. $$
Step Functions
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD