Final answer:
To estimate the area of the surface generated by revolving the curve y=cos(2x) about the x-axis using the trapezoidal rule, calculate the function values at equally spaced points over the interval [0, π/4] including the endpoints, form the corresponding trapezoids, find their areas, and sum them for the approximate surface area.
Step-by-step explanation:
The question asks us to estimate the area of the surface generated by revolving the curve y=cos(2x), with the limits 0≤x≤π/4 around the x-axis using the trapezoidal rule with five subdivisions. To estimate this area, we would typically use the formula for the surface area of revolution, which involves integrating the function along the given x-limits. However, the trapezoidal rule is a numerical method which involves dividing the interval into a number of trapezoids, calculating their areas, and summing. Since we are asked to use five subdivisions, we would calculate the function values at the endpoints and the four additional points equally spaced within the interval [0, π/4], then use these values to find the areas of the trapezoids formed and sum these to estimate the total surface area.