Work done equals area under force-extension curve

Steps:

• Identify graph as force vs. extension (length change) for spring.
• Recall work done $W = \int F \, dx$, area under curve from zero to final extension.
• Assume P is triangular area under linear Hooke's law line; Q is another region (e.g., beyond elastic limit).
• Conclude work for elastic stretching is just P, as total deformation work excludes plastic if Q is that.

Why A is correct:

• Area P is the integral of force over elastic extension, matching $W = \frac{1}{2} k x^2$ for Hooke's law.

Why the others are wrong:

• B: "P Q" implies multiplication, not additive area for work.
• C: Adding Q overcounts if Q is non-elastic or unloading region.
• D: Subtraction yields negative or irrelevant value, not physical work.

Final answer: A