Work done equals area under force-extension curve from extension d to 2d Steps: - Identify the graph as force (y-axis) versus extension (x-axis), linear per Hooke's law since extension doubles when force doubles. - Work done by force from W to 2W is ∫F dx from x=d to x=2d, the area under the curve in that interval. - Locate points: assume O at origin, R at (d, W), S at (2d, 2W); T, M mark the interval boundaries. - Calculate area as trapezoid TMRS: height (2d - d) = d, parallel sides W and 2W, area = (W + 2W)/2 × d = 1.5 Wd. Why D is correct: - TMRS is the trapezoidal area under the line from (d, W) to (2d, 2W), matching the definition of work as ∫F dx over that extension change. Why the others are wrong: - A. ORQ: Covers area from 0 to d, which is work for initial loading to W, not from W to 2W. - B. OQS: Includes full area from 0 to 2d, total work to 2W, exceeding the requested …