Final answer:
To find the area of the surface formed by rotating the curve y = √(9 - x^2) about the x-axis, we can use the formula for the surface area of revolution.
Step-by-step explanation:
To find the area of the surface formed by rotating the curve y = √(9 - x^2) about the x-axis, we can use the formula for the surface area of revolution. This formula is given by S = 2π ∫ (y * √(1 + (dy/dx)^2)) dx, where y is the curve and dx is the differential of x.
First, we need to find dy/dx, which is the derivative of y with respect to x. Differentiating y = √(9 - x^2) gives us dy/dx = -x/√(9 - x^2).
Next, we substitute y and dy/dx into the surface area formula and integrate from x = -1 to x = 2. Evaluating the integral gives us the area of the resulting surface.