The surface is generated by rotating the curve around the x-axis.
Take a vertical strip of width Δx.
the incremental area is 2πyΔs
where Δs = sqrt(1+(dy/dx)²).
let
y(x)=sqrt(1+5x),
y'(x)=5/(2sqrt(1+5x)
(y'(x))²=25/(4(1+5x))
So
Total surface area
7
=∫y*sqrt(1+y'²)dx
1
=∫sqrt(1+5x)sqrt(1+(5/(2sqrt(1+5x))^2)dx
=∫sqrt(20x+29)/2dx
=(20x+29)^(3/2)/60 from 1 to 7
=30.9
Check my arithmetic.
Find the exact area of the surface obtained by rotating the curve about the x-axis.
y = sqrt(1+5x) from 1<x<7
1 answer