6.3-bo'lim : Halqali ovoz balandligi

1-16-masalalar uchun disklar/halqalar usulidan foydalanib, berilgan egri chiziqlar bilan chegaralangan hududni berilgan o'q atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlang.

1. \(y = 2{x^2}\), \(y = 8\) va \(y\) o'qi bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
2. \(y = 2{x^2}\), \(y = 8\) va \(y\) o'qi bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
3. \(y = 2{x^2}\), \(x = 2\) va \(x\) o'qi bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
4. \(y = 2{x^2}\), \(x = 2\) va \(x\) o'qi bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
5. \(x = {y^3}\), \(x = 8\) va \(x\) o'qi bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
6. \(x = {y^3}\), \(x = 8\) va \(x\) o'qi bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
7. \(x = {y^3}\), \(y = 2\) va \(y\) o'qi bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
8. \(x = {y^3}\), \(y = 2\) va \(y\) o'qi bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
9. \(y = \frac{1}{{{x^2}}}\), \(y = 9\), \(x = - 2\), \(\displaystyle x = - \frac{1}{3}\) bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
10. \(y = \frac{1}{{{x^2}}}\), \(y = 9\), \(x = - 2\), \(\displaystyle x = - \frac{1}{3}\) bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
11. \(y = 4 + 3{{\bf{e}}^{ - x}}\), \(y = 2\), \(\displaystyle x = \frac{1}{2}\) va \(x = 3\) bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
12. \(x = 5 - {y^2}\) va \(x = 4\) bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
13. \(y = 6 - 2x\), \(y = 3 + x\) va \(x = 3\) bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
14. \(y = 6 - 2x\), \(y = 3 + x\) va \(y = 6\) bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
15. \(y = {x^2} - 2x + 4\) va \(y = x + 14\) bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
16. \(x = {\left( {y - 3} \right)^2}\) va \(x = 16\) bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
17. \(y = 2{x^2}\), \(y = 8\) va \(y\) o'qi bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun disklar/halqalar usulidan foydalaning.
    1. \(x = 3\) liniyasi
    2. qator \(x = - 2\)
    1. qator \(y = 11\)
    2. \(y = - 4\) liniyasi
18. \(x = {y^2} - 6y + 9\) va \(x = - {y^2} + 6y - 1\) bilan chegaralangan hududni atrofida aylantirish orqali olingan qattiq jismning hajmini aniqlash uchun disklar/halqalar usulidan foydalaning.
    1. qator \(x = 10\)
    2. qator \(x = -3\)
19. Uchburchakni \(\left( {3,2} \right)\), \(\left( {7,2} \right)\) va \(\left( {7,14} \right)\) uchlari atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun disklar/halqalar usulidan foydalaning.
    1. qator \(x = 12\)
    2. qator \(x = 2\)
    3. \(x = -1\) liniyasi
    1. \(y = 14\) liniyasi
    2. \(y = 1\) liniyasi
    3. qator \(y = -3\)
20. \(y = 4 + 3{{\bf{e}}^{ - x}}\), \(y = 2\), \(\displaystyle x = \frac{1}{2}\) va \(x = 3\) bilan chegaralangan hududni taxminan aylantirish orqali olingan qattiq jismning hajmini aniqlash uchun disklar/halqalar usulidan foydalaning.
    1. \(y = 7\) liniyasi
    2. qator \(y = 1\)
    3. \(y = -3\) liniyasi
21. \(x = 3 + {y^2}\) va \(x = 2y + 11\) bilan chegaralangan hududni atrofida aylantirish orqali olingan qattiq jismning hajmini aniqlash uchun disklar/halqalar usulidan foydalaning.
    1. qator \(x = 23\)
    2. qator \(x = 2\)
    3. \(x = -1\) liniyasi
22. \(y = 5 + \sqrt x \), \(y = 5\) va \(x = 4\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun disklar/halqalar usulidan foydalaning.
    1. qator \(y = 8\)
    2. \(y = 2\) liniyasi
    3. qator \(y = -2\)
23. \(y = 10 - 2x\), \(y = x + 1\) va \(y = 7\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun disklar/halqalar usulidan foydalaning.
    1. qator \(x = 8\)
    2. qator \(x = 1\)
    3. qator \(x = -4\)
24. \(y = - {x^2} - 2x - 5\) va \(y = 2x - 17\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun disklar/halqalar usulidan foydalaning.
    1. qator \(y = 3\)
    2. qator \(y = -1\)
    3. qator \(y = -34\)
25. \(x = - 2{y^2} - 3\) va \(x = - 5\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun disklar/halqalar usulidan foydalaning.
    1. qator \(x = 4\)
    2. qator \(x = -2\)
    3. qator \(x = -9\)