Question

If \[ x = \int_0^y \frac{1}{\sqrt{1+9t^2}} \, dt \quad \text{and} \quad \frac{d^2 y}{dx^2} = ay, \] then \( a \) is equal to:

• A. \( 3 \)
• B. \( 6 \)
• C. \( 9 \)
• D. \( 1 \)

Hint:

For integrals defining inverse functions: \begin{itemize} \item Use Fundamental Theorem of Calculus. \item Convert \( dx/dy \) to \( dy/dx \). \item Apply chain rule carefully. \end{itemize}

Answer 1

The Correct Option is C