Please, help me solve these problems without using Laplace. So on http://mathworld.wolfram.com/DeltaFunction.html I found these fundamenetal properties that I thought I could use to solve the problems, but I'm not sure if I applied them correctly. Here is my work so far for part a, but I don't know how to approach part b because the bounds are different. Thank you in advance.
2026-03-26 09:38:28.1774517908
Integral involving an impulse function (no Laplace)
53 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in INTEGRATION
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- How to integrate $\int_{0}^{t}{\frac{\cos u}{\cosh^2 u}du}$?
- Show that $x\longmapsto \int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha }}dy$ is integrable.
- How to find the unit tangent vector of a curve in R^3
- multiplying the integrands in an inequality of integrals with same limits
- Closed form of integration
- Proving smoothness for a sequence of functions.
- Random variables in integrals, how to analyze?
- derive the expectation of exponential function $e^{-\left\Vert \mathbf{x} - V\mathbf{x}+\mathbf{a}\right\Vert^2}$ or its upper bound
- Which type of Riemann Sum is the most accurate?
Related Questions in DIRAC-DELTA
- What is the result of $x(at) * δ(t-k)$
- Solution to ODE with Dirac Delta satisfies ODE
- How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?
- Approximating derivative of Dirac delta function using mollifiers
- How to prove this Dirac delta limit representation is correct?
- $\int_{-\epsilon}^\epsilon\delta(f(x))g(x)dx=\frac{g(0)}{f'(0)}$?
- Properties about Dirac Delta derivative
- Dirac / Fourier relation
- Prove that $\frac{1}{\epsilon}\int_{\mathbb{R}}f(t).\exp\left(\frac{-\pi(x-t)^2}{\epsilon^2}\right)dt \xrightarrow{\epsilon \to 0}f(x) $
- Integral involving delta functions and vector quantities
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
You seem to be going in the right direction. To my understanding, the limits of integration do not have to be the same. The only requirement is that the limits enclose the "position" of the impulse. For example: $$\int_{-\infty}^{\infty} f(t)\delta(t-2)dt = f(2) $$ This encloses the "position" of the impulse $$\int_1^3 f(t)\delta(t-2)dt = f(2) $$ This does not $$\int_3^4 f(t)\delta(t-2)dt = 0 $$