tolongg dongg plisss hitunglah volume benda putar yang terjadi, bila daerah'' di bawah ini diputar 360 terhadap sumbu Y: a. xy=1, garis y=2, y=6, dan sumbu Y b.

1.
xy = 1, x = 1/y
Volume :
[tex]\displaystyle \pi \int_2^6(\frac{1}{y})^2$ $dy=\pi \int_2^6\frac{1}{y^2}$ $dy=\pi\int_2^6y^{-2}$ $dy \\ \pi(-y^{-1}]_2^6)=\pi((-6^{-1})-(-2^{-1}))=\pi(-\frac{1}{6}+\frac{1}{2})=\frac{1}{3}\pi[/tex]
2.
Cari titik potong y = 9-x^2, x = akar(9-y)
akar(9-y) = 0, didapat titik potong y = 9
Jadi,
[tex]\pi \int_{-9}^9\sqrt{9-y}^2$ $dy = \pi \int_{-9}^9 9-y$ $dy=\pi (9y-\frac{y^2}{2}]_{-9}^9) \\ \pi ((9.9-\frac{9^2}{2})-(9(-9)-\frac{(-9)^2}{2}))=\pi(\frac{81}{2}+\frac{243}{2})=162\pi[/tex]