(Arc length and surface area) Rotate the graph of 𝑔(𝑥)=𝑒^(−9𝑥) on the interval [0,7] about the x-axis to generate a surface with x square units.

Answer 1

S = ∫₀⁷2πg(x)√[1 + (g'(x))²]dx = 2π∫₀⁷e^-9x√(1 + 81e^-18x)dx = 19.55

To evaluate integral I use TI-84