Final answer:
The question involves calculating the surface area of a solid of revolution, specifically the curve y = √(x+1) revolved around the x-axis from x=1 to x=11, using integration.
Step-by-step explanation:
The student is asking how to find the surface area generated by revolving a curve around the x-axis. The curve is defined by the function y = √(x+1) for the interval 1 ≤ x ≤ 11. To solve this, we'll use the formula for the surface area of a surface of revolution, which integrates 2πy over the given interval while multiplying by the derivative of the function with respect to x, dy/dx. This takes into account the circumference of each infinitesimal 'disk' and the rate at which the radius changes as we move along the curve.
The calculation will involve setting up the integral ∫2πy √(1+(dy/dx)^2) dx from x = 1 to x = 11, solving for dy/dx from the original function, and then evaluating the integral to determine the total surface area.