4. (Harder.) Evaluate the following integrals, where 8(z) is the Dirac delta function:

Ĵ6(2² - 9) dz;

[*(z) 6(2²-

d) [e¹² 8'(x) dx.

a)

f(x) 6'(x) dx;

b)

(x) 8(x²-a²) dx (a > 0);

8'(x) is the derivative of the delta function. If you don't know what to do with the

derivative of a delta function, why not try integration by parts?