Sifting Property (Dirac Delta), please check these

[IHave]

Homework Statement

use the sifting property of the dirac delta function to evaluate the following integrals.

a) integral from -inf to inf sin(t) delta(t-pi/2)dt

b) integral from 0 to 2 e^(2t) delta(t-1)dt

c) integral from 0 to pi e^tan(theta) delta(theta- 3pi/4)d(theta)

d) integral from -inf to inf cos^(2)(theta) delta(theta+y)d(theta)

Homework Equations

integral from -inf to inf f(x) delta(x-x0)dx=f(x0)

The Attempt at a Solution

solutions:

a) 1
b) e^2
c) e^tan(theta)
d) cos^(2)(y)

are these solutions correct?

 

[vela]

Your answer for c is wrong.