Chapter 8.11, Problem 21P

Make use of the operator equations (11.19) and previous equations to evaluate the following integrals.

(a) ${\displaystyle {\int }_0^3(5x-2)}\delta (2-x)dx$ (b) ${\displaystyle {\int }_0^{\infty }\varphi }(x)\delta \left(x^2-a^2\right)dx$

(c) ${\displaystyle {\int }_{-1}^1\cos }x\delta (-2x)dx$ (d) ${\displaystyle {\int }_{-\pi /2}^{\pi /2}\cos }x\delta (\sin x)dx$