Evaluate the following integral,where is the usefulness of the delta function in the evaluation?
$$\int_{-\infty}^{\infty} f(r)\nabla\frac{\vec{r}-i}{(r-i)^3} dr$$
2026-03-26 05:54:22.1774504462
What is the solution to the following integral? Dirac Delta function must be invoked at some point.
39 Views Asked by user23086 https://math.techqa.club/user/user23086/detail AtRelated Questions in DEFINITE-INTEGRALS
- How can I prove that $\int_0^{\frac{\pi}{2}}\frac{\ln(1+\cos(\alpha)\cos(x))}{\cos(x)}dx=\frac{1}{2}\left(\frac{\pi^2}{4}-\alpha^2\right)$?
- Closed form of integration
- Integral of ratio of polynomial
- An inequality involving $\int_0^{\frac{\pi}{2}}\sqrt{\sin x}\:dx $
- How is $\int_{-T_0/2}^{+T_0/2} \delta(t) \cos(n\omega_0 t)dt=1$ and $\int_{-T_0/2}^{+T_0/2} \delta(t) \sin(n\omega_0 t)=0$?
- Roots of the quadratic eqn
- Area between curves finding pressure
- Hint required : Why is the integral $\int_0^x \frac{\sin(t)}{1+t}\mathrm{d}t$ positive?
- A definite integral of a rational function: How can this be transformed from trivial to obvious by a change in viewpoint?
- Integrate exponential over shifted square root
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
Related Questions in ELECTROMAGNETISM
- Kirchhoff's Law and Highest Potential Node
- can I solve analytically or numerically the equation $\vec{\nabla}\cdot\vec{J}=0$ with the following boundaries?
- How to make the Biot-Savart law to go along a spiral shaped coil?
- I am currently reading Special Relativity by Woodhouse, I need help with understanding divergence of magnetic fields
- Calculation of capacitance between two cylinders
- Find directions where current is maximal
- What is the relation between 2d Fourier Transform and Plane Waves?
- Magnetic force term in Kobe's derivation of Maxwell's equations
- Expansion of 1/R
- Gauss' law and a half-cylinder
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?