Answer:
The area of this revolted surface is 36π
Step-by-step explanation:
To obtain the area of a revolted surface, you have to define:
1) which is the axis on which the surface is revolted: this defines the limits on that axis or hight of the surface. In this case x∈[0;2]
2) which is the expression of the radius of the revolted surface and its dependence with the hight. In this case, the radius expression could be Y=4x+5
3) Define the angular variable: If this is a fully revolted surface, the angular variable will go from 0 to 2π
Now we can obtain the area with a double integral:
[tex]A=\int\limits^{2}_0 { \int\limits^{2\pi}_0 {r} \, d \varphi } \, dx =\int\limits^{2}_0 { \int\limits^{2\pi}_0 {4x+5} \, d \varphi } \, dx =\int\limits^{2}_0 { (2\pi)(4x+5)} \, dx=36\pi[/tex]
