Page 235 - Schaum's Outline of Differential Equations

218 THE LAPLACE TRANSFORM [CHAP. 21

2
F(s) = 2/0 - 4), and then, from Property 21.5 that

21.21. Prove that if fix +K>) = -f(x), then

Since

f(x) is periodic with period 2(0. Then, using Property 21.6 with to replaced by 2(0, we have

Substituting y = x - to into the second integral, we find that

The last integral, upon changing the dummy variable of integration back to x, equals

Thus,

Fig. 21-2