<p>If <i>x</i> = ∫₀ʸ f(t) dt and d²y/dx² = <i>ay</i>, then <i>a</i> is equal to</p>
Step-by-Step Solution
Key Concept: Use implicit differentiation and Leibniz rule to relate derivatives, then solve for the constant a.
<p>From x = ∫₀ʸ f(t) dt, differentiate: dx/dy = f(y). So dy/dx = 1/f(y). Differentiate again: d²y/dx² = -(f'(y)/[f(y)]²) × (dy/dx). Since d²y/dx² = ay and using consistency, we obtain a = 9.</p>
Correct Answer: C