bogenlänge-einer-ebenen-kurve

7.44) $f(x)=a\ast x^2+bx+c$ $f(0)=5\Rightarrow c=5$ $f(20)=0$ $f(-20)=0$ Nlöse $f(x)=-\frac{1}{80x}+5$ $f^{\prime }(x)=-\frac{1}{40x}$ $S=2\ast {\int }_0^{20}\sqrt{1+\frac{x^2}{40}}dx\approx 41.6m$ 7.45) Hineweis: ${\cosh }^{2}x-{\sinh }^{2}x=1$ ${\cosh }^{2}x=1+{\sinh }^{2}x$