Chapter 8: Q4P (page 458)

Show that $\int_{- \infty}^{\infty} f_{n} (t) d t = 1$ for the functions $f_{n} (t)$ in Figures 11.3 and 11.4.

Short Answer

Expert verified

The given function is verified

Step by step solution

Given information

The given expressions are $\int f_{x} (t) d t = 1$ .

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)

Verify the given function

Show that

$\int f_{n} (t) d t = 1$

Where

$f_{n} (t) = n e^{- n (i - r_{o})} t > I_{0}$

$f_{n} (f) = 0$

Otherwise

$\int_{f_{n}} (t) d t = \int_{i} n e^{- n (t - n_{0})} d t$

Solve further

$\int_{0} f_{n} (t) d t = n e^{n h_{n}} (\frac{e^{- π}}{- π}) \int f_{n} (t) d t = e^{n + 0 - n + 0} \int f_{n} (t) d t = 1$

Thus, verified.

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Show that $\int_{- \infty}^{\infty} f_{n} (t) d t = 1$ for the functions $f_{n} (t)$ in Figures 11.3 and 11.4.

Short Answer

Step by step solution

Given information

Definition of Laplace Transformation

Verify the given function

One App. One Place for Learning.

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

Short Answer

Step by step solution

Given information

Definition of Laplace Transformation

Verify the given function

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Wave Optics

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Study anywhere. Anytime. Across all devices.

Show that $\int_{- \infty}^{\infty} f_{n} (t) d t = 1$ for the functions $f_{n} (t)$ in Figures 11.3 and 11.4.