Regn ut (sint∗1)(t)(\sin t*1)(t)(sint∗1)(t).
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(sint∗1)(t)=∫0tsinτ dτ=[−cosτ]0t=1−cost(\sin t*1)(t)=\int_0^t \sin\tau\,d\tau=[-\cos\tau]_0^t=1-\cos t(sint∗1)(t)=∫0tsinτdτ=[−cosτ]0t=1−cost. Kontroll: 1s2+1⋅1s=1s(s2+1)=L{1−cost}\displaystyle \frac{1}{s^2+1}\cdot\frac{1}{s}=\frac{1}{s(s^2+1)}=\mathcal{L}\{1-\cos t\}s2+11⋅s1=s(s2+1)1=L{1−cost}. ✓
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