Integral of unit step function [closed]

1. What is the integral of unit step function?
2. Is unit step function discontinuous?
3. What is the integral of a ramp function?
4. What is the integration of impulse function?

What is the integral of unit step function?

In other words, the integral of a unit step is a "ramp" function. This function is 0 for all values that are less than zero, and becomes a straight line at zero with a slope of +1.

Is unit step function discontinuous?

Mathematical Preliminaries

The Heaviside step function H(x), also called the unit step function, is a discontinuous function, whose value is zero for negative arguments x < 0 and one for positive arguments x > 0, as illustrated in Fig. 2.2.

What is the integral of a ramp function?

The integration of the unit ramp is a parabolic signal

p ( t ) = ∫ t d t = t 2 2. A parabolic signal is expressed as. p ( t ) = t 2 2 ; t ≥ 0 0 ; e l s e w h e r e.

What is the integration of impulse function?

So the integral of of an impulse function alone over any interval would be 1 since regardless of the shift 'a', of f(x)*d(x-a)dx = 1 for all x since f(x) is the constant function 1.