Dirac Delta Function
Dirac Delta Function Exercise 1 : Basic Delta Integrals Evaluate the following integrals: $\displaystyle \int_{2}^{6} (3x^2 - 2x - 1) , \delta(x - 3) , dx$ $\displaystyle \int_{0}^{5} \cos x ; \delta(x - \pi) , dx$ $\displaystyle \int_{-1}^{3} x^3 , \delta(x + 1) , dx$ $\displaystyle \int_{-\infty}^{\infty} \ln(x + 3) , \delta(x + 2) , dx$ $\displaystyle \int_{0}^{\infty} e^{-x} , \delta(x - 2) , dx$ Exercise 2 : Delta with Scaled & Shifted Arguments Use $\delta(ax) = \frac{1}{|a|}\delta(x)$ and similar properties to evaluate: ...