Let `C` be the curve ` y = 3 sqrt( x ) ` for `2.6 le x le 3.7`.
Find the surface area of revolution about the `x`-axis of `C`.
Surface area `= int_2.6^3.7 f( x ) \ dx` where
`f( x ) =`
Write your answer in this format: `2 pi * 3 sqrt( x + 3^2 / 4 )`
Now integrate to find surface area
Surface area `= int_2.6^3.7 f( x ) \ dx =`
To find the surface area of revolution, recall the formula for surface area when rotating a curve around the `x`-axis. Consider how to express the derivative `dy/dx` for the given function, and how it fits into the surface area formula. Remember to set up your integral carefully, paying attention to the given bounds.
Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c
Be sure your variables match those in the question
`2 pi * 3 sqrt( x + 3^2 / 4 )`
Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4) Enter DNE for Does Not Exist, oo for Infinity
`2 pi * 3 sqrt( x + 3^2 / 4 )`
48.161783454023