Find the area of the surface obtained by rotating the curve y=(3/4)(x), 0 ≤ x≤ 1, around the x-axis

A) 15pi/16
B) 16pi
C) 2pi/3
D) 16pi/3


Thank you.

Since we are rotating the region about the x-axis, the surface area equals
∫ 2πy √(1 + (dy/dx)^2) dx
= ∫(x = 0 to 1) 2π * (3x/4) * √(1 + (3/4)^2) dx
= ∫(x = 0 to 1) 2π * (3x/4) * (5/4) dx
= (15π/16) * ∫(x = 0 to 1) 2x dx
= 15π/16.

I hope this helps!