Find the exact area of the surface obtained by rotating the curve about the x-axis

Question

y = square root(1 + 3x) , 1 ≤ x ≤ 9?

Answer 1

For rotation about the x - axis, the surface area formula : .

For rotation about the y - axis, the surface area formula : .

The rotating curve y = √(1 + 3x) about the x - axis and the interval [a, b] = [1, 9].

y = √(1 + 3x) ⇒ y' = 3/[2√(1 + 3x)]

Apply formula : .

.

Therefore, area of the surface obtained by rotating the given curve about the x - axis is .