6.4-bo'lim : Silindrli hajm

1-14-masalalar uchun silindrlar 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. \(\displaystyle y = \frac{1}{x}\), \(\displaystyle y = \frac{1}{3}\) va \(\displaystyle x = \frac{1}{2}\) bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
10. \(\displaystyle y = \frac{1}{x}\), \(\displaystyle y = \frac{1}{3}\) va \(\displaystyle x = \frac{1}{2}\) bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
11. \(y = 6 - 2x\), \(y = 3 + x\) va \(x = 3\) bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
12. \(y = 6 - 2x\), \(y = 3 + x\) va \(y = 6\) bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
13. \(y = {x^2} - 6x + 11\) va \(y = 6\) bilan chegaralangan hududni \(y\) o'qi atrofida aylantiring.
14. \(x = {y^2} - 8y + 19\) va \(x = 2y + 3\) bilan chegaralangan hududni \(x\) o'qi atrofida aylantiring.
15. \(y = 2{x^2}\), \(y = 8\) va \(y\) o'qi bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. qator \(x = 3\)
    2. \(x = -2\) liniyasi
    1. qator \(y = 11\)
    2. qator \(y = -4\)
16. \(x = {y^3}\), \(x = 8\) va  \(x\) o'qi bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. \(x = 10\) liniyasi
    2. \(x = -3\) liniyasi
    1. qator \(y = 3\)
    2. \(y = -4\) liniyasi
17. \(x = {y^2} - 6y + 9\) va \(x = - {y^2} + 6y - 1\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. \(y = 7\) liniyasi
    2. qator \(y = -2\)
18. Uchburchakni \(\left( {3,2} \right)\), \(\left( {7,2} \right)\) va \(\left( {7,14} \right)\) uchlari atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. \(x = 12\) liniyasi
    2. qator \(x = 2\)
    3. qator \(x = -1\)
    1. qator \(y = 14\)
    2. qator \(y = 1\)
    3. \(y = -3\) liniyasi
19. \(y = 4 + 3{{\bf{e}}^{ - x}}\), \(y = 2\), \(x = \frac{1}{2}\) va \(x = 3\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. \(x = 5\) liniyasi
    2. qator \(\displaystyle x = \frac{1}{4}\)
    3. qator \(x = - 1\)
20. \(x = {y^2} - 8y + 19\) va \(x = 2y + 3\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. \(y = 9\) liniyasi
    2. qator \(y = 1\)
    3. qator \(y = -3\)
21. \(y = 5 + \sqrt {x - 3} \), \(y = 5\) va \(x = 4\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. qator \(x = 9\)
    2. qator \(x = 2\)
    3. qator \(x = -1\)
22. \(y = - {x^2} - 10x + 6\) va \(y = 2x + 26\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. qator \(x = 2\)
    2. qator \(x = -1\)
    3. qator \(x = -14\)
23. \(x = {y^2} - 10y + 27\) va \(x = 11\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. qator \(y = 10\)
    2. qator \(y = 1\)
    3. qator \(y = -3\)
24. \(y = 2{x^2} + 1\), \(y = 7 - x\), \(x = 3\) va \(\displaystyle x = \frac{3}{2}\) bilan chegaralangan hududni atrofida aylantirish natijasida olingan qattiq jismning hajmini aniqlash uchun silindrlar usulidan foydalaning.
    1. qator \(x = 6\)
    2. qator \(x = 1\)
    3. qator \(x = -2\)