Asosiy tarkibga o'tish

8.2-bo'lim : Er yuzasi

  1. \(y = 7x + 2\) , \( - 5 \le y \le 0\) ni \(x\) o'qi atrofida aylantirish orqali olingan ob'ektning sirt maydoni uchun integralni o'rnating, lekin baholamang,
    1. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
    2. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
  2. \(y = 1 + 2{x^5}\) , \(0 \le x \le 1\) ni \(x\) o'qi atrofida aylantirish orqali olingan ob'ektning sirt maydoni uchun integralni o'rnating, lekin baholamang,
    1. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
    2. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
  3. \(x = {{\bf{e}}^{2y}}\) , \( - 1 \le y \le 0\) ni \(y\) o'qi atrofida aylantirish orqali olingan ob'ektning sirt maydoni uchun integralni o'rnating, lekin baholamang,
    1. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dy}}{{dx}}} \right]}^2}} \,dx\)
    2. \(\displaystyle ds = \sqrt {1 + {{\left[ {\frac{{dx}}{{dy}}} \right]}^2}} \,dy\)
  4. \(y = \cos \left( {\displaystyle \frac{1}{2}x} \right)\) , \(0 \le x \le \pi \) atrofida aylanish natijasida olingan ob'ektning sirt maydoni uchun integralni o'rnating, lekin baholamang.
    1. \(x\) o'qi
    2. \(y\) o'qi
  5. \(x = \sqrt {3 + 7y} \) , \(0 \le y \le 1\) atrofida aylanish natijasida olingan ob'ektning sirt maydoni uchun integralni o'rnating, lekin baholamang.
    1. \(x\) o'qi
    2. \(y\) o'qi
  6. \(\displaystyle y = \frac{1}{4}\sqrt {6x + 2} \) , \(\displaystyle \frac{{\sqrt 2 }}{2} \le y \le \frac{{\sqrt 5 }}{2}\) ni \(x\) o'qi atrofida aylantirish orqali olingan ob'ektning sirt maydonini toping.
  7. \(y = 4 - x\) , \(1 \le x \le 6\) ni \(y\) o'qi atrofida aylantirish orqali olingan ob'ektning sirt maydonini toping.
  8. \(x = 2y + 5\) , \( - 1 \le x \le 2\) ni \(y\) o'qi atrofida aylantirish orqali olingan ob'ektning sirt maydonini toping.
  9. \(x = 1 - {y^2}\) , \(0 \le y \le 3\) ni \(x\) o'qi atrofida aylantirish orqali olingan ob'ektning sirt maydonini toping.
  10. \(x = {{\bf{e}}^{2y}}\) , \( - 1 \le y \le 0\) ni \(y\) o'qi atrofida aylantirish orqali olingan ob'ektning sirt maydonini toping.
  11. \(y = \cos \left( {\displaystyle \frac{1}{2}x} \right)\) , \(0 \le x \le \pi \) ni \(x\) o'qi atrofida aylantirish orqali olingan ob'ektning sirt maydonini toping.