Question:medium

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:

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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}

Updated On: Mar 2, 2026

\( 3 \)
\( 6 \)
\( 9 \)
\( 1 \)

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The Correct Option is C

Solution and Explanation

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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:

Show Hint

The Correct Option is C

Solution and Explanation

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