Hitunglah volume benda putar yang terjadi jika daerah-daerah berikut ini diputar sejauh 360° terhadap sumbu X.
a. y=x-1, sumbu X, sumbu Y, dan y=2
a. y=x-1, sumbu X, sumbu Y, dan y=2
xkuadratz
![V= \pi (\int\limits^3_1 {(2^2-(x-1)^2)} \, dx+ \int\limits^1_0 {2^2} \, dx ) \\ \\ =\pi (\int\limits^3_1 {(3-x^2+2x)} \, dx+ \int\limits^1_0 {4} \, dx \\ \\ =((3x- \frac{x^3}{3}+x^2) \left[\begin{array}{ccc}3\\1\end{array}\right] +4x \left[\begin{array}{ccc}1\\0\end{array}\right] ) \pi \\ \\ =(((9-9+9)-(3- \frac{1}{3}+1 ))+4) \pi \\ \\ =9 \frac{1}{3} \pi](https://tex.z-dn.net/?f=V%3D+%5Cpi++%28%5Cint%5Climits%5E3_1+%7B%282%5E2-%28x-1%29%5E2%29%7D+%5C%2C+dx%2B+%5Cint%5Climits%5E1_0+%7B2%5E2%7D+%5C%2C+dx++%29+%5C%5C+%5C%5C++%3D%5Cpi++%28%5Cint%5Climits%5E3_1+%7B%283-x%5E2%2B2x%29%7D+%5C%2C+dx%2B+%5Cint%5Climits%5E1_0+%7B4%7D+%5C%2C+dx+%5C%5C++%5C%5C+%3D%28%283x-+%5Cfrac%7Bx%5E3%7D%7B3%7D%2Bx%5E2%29++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C1%5Cend%7Barray%7D%5Cright%5D++%2B4x+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C0%5Cend%7Barray%7D%5Cright%5D+%29+%5Cpi++%5C%5C++%5C%5C+%3D%28%28%289-9%2B9%29-%283-+%5Cfrac%7B1%7D%7B3%7D%2B1+%29%29%2B4%29+%5Cpi++%5C%5C++%5C%5C+%3D9+%5Cfrac%7B1%7D%7B3%7D++%5Cpi+ "V= \pi (\int\limits^3_1 {(2^2-(x-1)^2)} \, dx+ \int\limits^1_0 {2^2} \, dx ) \\ \\ =\pi (\int\limits^3_1 {(3-x^2+2x)} \, dx+ \int\limits^1_0 {4} \, dx \\ \\ =((3x- \frac{x^3}{3}+x^2) \left[\begin{array}{ccc}3\\1\end{array}\right] +4x \left[\begin{array}{ccc}1\\0\end{array}\right] ) \pi \\ \\ =(((9-9+9)-(3- \frac{1}{3}+1 ))+4) \pi \\ \\ =9 \frac{1}{3} \pi")
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