12.9-bo'lim: Vektor funktsiyalari bilan yoy uzunligi

1 va 2 masalalar uchun vektor funksiyaning berilgan oraliqdagi uzunligini aniqlang.

1. \( - 6 \le t \le 8\) dan \(\vec r\left( t \right) = \left( {3 - 4t} \right)\vec i + 6t\,\vec j - \left( {9 + 2t} \right)\vec k\). Yechim
2. \(0 \le t \le 2\) dan \(\vec r\left( t \right) = \left\langle {\frac{1}{3}{t^3},4t,\sqrt 2 {t^2}} \right\rangle \). Yechim

3 va 4-masalalar uchun berilgan vektor funksiya uchun yoy uzunligi funksiyasini toping.

1. \(\vec r\left( t \right) = \left\langle {{t^2},2{t^3},1 - {t^3}} \right\rangle \) Yechim
2. \(\vec r\left( t \right) = \left\langle {4t, - 2t,\sqrt 5 \,\,{t^2}} \right\rangle \) Yechim
3. 20 masofani bosib o‘tganimizdan keyin \(\vec r\left( t \right) = \left\langle {{t^2},2{t^3},1 - {t^3}} \right\rangle \) tomonidan berilgan egri chiziqning qayerida ekanligimizni aniqlang. Yechim