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Chapter 8: Q4P (page 458)

Show that鈭�-鈭�鈭�fn(t)dt=1for the functionsfn(t)in Figures 11.3 and 11.4.

Short Answer

Expert verified

The given function is verified

Step by step solution

01

Given information

The given expressions are鈭�fxtdt=1.

02

Definition of Laplace Transformation

A transformation of a function f(x) into the function g(t) that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.

The inverse Laplace transform of a function F(s) is the piecewise-continuous and exponentially-restricted real function f(t)

03

Verify the given function

Show that

鈭�fn(t)dt=1

Where

fn(t)=ne-ni-rot>I0

fn(f)=0

Otherwise

鈭�fn(t)dt=鈭�ine-nt-n0dt

Solve further

鈭�0fntdt=nenhne-蟺-蟺鈭�fntdt=en+0-n+0鈭�fntdt=1

Thus, verified.

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Most popular questions from this chapter

By using Laplace transforms, solve the following differential equations subject to the given initial conditions.

y''+2y'+10y=-6e-tsin3t,y0=0,y'0=1

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