Final answer:
To find the area of the surface obtained by rotating the curve y = 11x + 1 about the x-axis, we can use the formula for the surface area of a solid of revolution.
Step-by-step explanation:
To find the area of the surface obtained by rotating the curve y = 11x + 1 about the x-axis, we can use the formula for the surface area of a solid of revolution:
Surface Area = ∫2πy√(1 + (dy/dx)²) dx
In this case, the derivative of y = 11x + 1 is dy/dx = 11. Substituting these values into the formula, we get:
Surface Area = ∫2π(11x + 1)√(1 + 11²) dx
Simplifying and evaluating the integral gives:
Surface Area = 2π ∫(11x + 1)√122 dx