請個位大大幫我一個忙,小弟我不知怎麼解這題數學. 謝謝!
證明 verify L {y"}= s^2F(s)-sy(0)-Y'(0)
∫ f''(t) e^(-st) dt
=∫ e^(-st) d f'(t)
= -f'(t) e^(-st) | (0,infinity) + s ∫ f'(t) e^(-st) dt
=-f'(0) + s ∫ e^(-st) d f(t)
=-f'(0)+s f(t) e^(-st) | (0,infinity) + s^2 ∫ f(t) e^(-st) dt
=-f'(0)-s f(0) + s^2 F(s)
2010-03-09 18:49:16 補充：
f'(t) e^(-st) | (0,infinity)
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Verified answer
∫ f''(t) e^(-st) dt
=∫ e^(-st) d f'(t)
= -f'(t) e^(-st) | (0,infinity) + s ∫ f'(t) e^(-st) dt
=-f'(0) + s ∫ e^(-st) d f(t)
=-f'(0)+s f(t) e^(-st) | (0,infinity) + s^2 ∫ f(t) e^(-st) dt
=-f'(0)-s f(0) + s^2 F(s)
2010-03-09 18:49:16 補充：
f'(t) e^(-st) | (0,infinity)