Introduction to Electrodynamics · Problem 1.45

Vector Analysis — David J. Griffiths

Physics · dirac-delta-function

Problem

Evaluate the following integrals: (a) ∫−22(2x+3) δ(3x) dx\int_{-2}^{2} (2x + 3)\,\delta(3x)\,dx. (b) ∫02(x3+3x+2) δ(1−x) dx\int_0^2 (x^3 + 3x + 2)\,\delta(1 - x)\,dx. (c) ∫−119x2 δ(3x+1) dx\int_{-1}^{1} 9x^2\,\delta(3x + 1)\,dx. (d) ∫−∞aδ(x−b) dx\int_{-\infty}^{a} \delta(x - b)\,dx.

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