Surface area of y=1+5x² rotated about y-axis

[danielatha4]

Homework Statement

Find the area of the surface obtained by rotating the curve y=1+5x² from x=0 to x=8 about the y-axis

Homework Equations

A_s=$$\int$$2$$\pi$$g(x)sqrt(1+[g'(x)]²)

The Attempt at a Solution

I changed the limits to suit the y direction, the lower limit becomes 1 and the upper 321. I solved x as a function of y in order to rotate around the y-axis and when I plug everything into the formula is becoems a really messy integral I can't solve. I'm sure there's an easier way.

 

[tiny-tim]

Hi danielatha4!

Why not just use ∫ 2πx √(1 + g'(x)²) dx ?