∫-∞^∞(t^2-1) δ(t) d t

Name: Problem 1, Chapter 7: Fundamentals of Differential Equations
Uploaded: 2020-07-16T12:48:02-08:00
Duration: 30 s
Channel: Sajin Shajee
Description: ∫-∞^∞(t^2-1) δ(t) d t

step 1 Okay, we have the integration of negative to break t squared minus one, delta t, ft is equal to

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Question

$\int_{-\infty}^{\infty}\left(t^{2}-1\right) \delta(t) d t$

   $\int_{-\infty}^{\infty}\left(t^{2}-1\right) \delta(t) d t$

Fundamentals of Differential Equations

R. Kent Nagle 9th Edition

Chapter 7, Problem 1

Instant Answer

Solved by Expert Sajin Shajee

07/16/2020

Step 1

In this case, the delta function is centered at t=0. Show more…

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$\int_{-\infty}^{\infty}\left(t^{2}-1\right) \delta(t) d t$

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Key Concepts

Dirac Delta Function

The Dirac delta function is not a function in the typical sense but rather a distribution that is zero everywhere except at a single point, where its integral over the entire real line equals one. It is used to model point sources and impulse responses in various areas of mathematics and physics.

Sifting Property

The sifting property is a key feature of the Dirac delta distribution that allows it to 'sample' or 'extract' the value of another function at a specific point. When integrated against a test function, the delta function 'picks out' the value of the test function at the location where the delta function is centered.

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