yield \(\text {length}(\gamma (-,t))=\sqrt{1+\left( \frac{\partial u}{\partial x}\right) ^{2}(c,t)}\cdot (b-a)=_{j}\sqrt{1+\varphi ^{2}(c,t)}\cdot (b-a)\) for some \(c\in [a,b]\) . the taylor formula with peano remainder applied to the function \(\...