Question: Define the integrals (I_{n}=int_{-infty}^{infty} x^{2 n} e^{-x^{2}} d x). Noting that (I_{0}=sqrt{pi}), a. Find a recursive relation between (I_{n}) and (I_{n-1}). b. Use this relation

Define the integrals \(I_{n}=\int_{-\infty}^{\infty} x^{2 n} e^{-x^{2}} d x\). Noting that \(I_{0}=\sqrt{\pi}\),

a. Find a recursive relation between \(I_{n}\) and \(I_{n-1}\).

b. Use this relation to determine \(I_{1}, I_{2}\), and \(I_{3}\).

c. Find an expression in terms of \(n\) for \(I_{n}\).

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