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+4x) about the x - axis and the interval [a, b] = [0, 4].

y = √(1+4x) ⇒ y = 2/√(1+4x)

Let (5+4x) = t² ⇒ 4dx = 2t dt ⇒ dx = (t/2) dt.