What is the value of the integral ∫−∞+∞𝑑𝑥4𝑥𝛿(𝑥−1)∫ −∞+∞​ dx4 x δ(x−1)?1248

The integral ∫−∞+∞𝑑𝑥4𝑥𝛿(𝑥−1) is a definite integral involving the Dirac delta function, δ(x−1). The Dirac delta function is a mathematical construct which is used to model an infinitely sharp peak at a certain point in a function, in this case at x=1.

The integral of a function multiplied by the Dirac delta function is simply the value of the function at the point where the Dirac delta function peaks.

So, in this case, we need to evaluate the function 4x at x=1.

4*1 = 4

So, the value of the integral ∫−∞+∞𝑑𝑥4𝑥𝛿(𝑥−1) is 4.