Question

Use Definition /.1.1. DEFINITION 7.1.1 Laplace Transform Let \( f \) be a function defined for \( t \geq 0 \). Then the integral \[ \mathscr{L}\{f(t)\}=\int_{0}\ᶦⁿᶠᵗʸ e⁻ˢ ᵗ f(t) d t \] is said t

A) To find the integral of f(t) from 0 to +[infinity].
B) To analyze the function f(t) in the time domain.
C) To convert a function from the time domain to the frequency domain.
D) To calculate the average value of f(t) over an infinite interval.

Answer 1

The Laplace Transform is used to convert a function from the time domain to the frequency domain, corresponding to option C in the given choices.

Step-by-step explanation:

The Laplace Transform is a mathematical technique used to convert a function from the time domain to the frequency domain. It is defined by the integral shown in Definition 7.1.1: \( \mathscr{L}\{f(t)\}=\int_{0}^{\infty} e^{-st} f(t) dt \), where s is a complex number frequency parameter. The correct answer to what the Laplace Transform is used for is option C) To convert a function from the time domain to the frequency domain.