8.1-bo'lim: Ark uzunligi

1. \(y = \sqrt {x + 2} \) , \(1 \le x \le 7\) uzunligi uchun integralni sozlang, lekin baholamang,
   1. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
   2. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
   Yechim
2. \(x = \cos \left( y \right)\), \(0 \le x \le \frac{1}{2}\) uzunligi uchun integralni sozlang, lekin baholamang,
   1. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
   2. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
   Yechim
3. \(y = 7{\left( {6 + x} \right)^{\frac{3}{2}}}\) , \(189 \le y \le 875\) uzunligini aniqlang. Yechim
4. \(x = 4{\left( {3 + y} \right)^2}\) , \(1 \le y \le 4\) uzunligini aniqlang. Yechim