Question Bank NAT • 1 Mark Section 1: Mathematical Physics Fourier and Laplace transforms

QB_PH_016: Fourier and Laplace transforms

Question Statement

The value of the integral $\int_{-\infty}^\infty (x^3 + 4x + 7) \delta(x - 2) dx$ is:
Correct Answer
23, 23
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: Sifting property: $f(2) = 2^3 + 4(2) + 7 = 8 + 8 + 7 = 23$.
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