Integral of sinc²(mx)

Correct Answer

B — 1/m

Concept and Reasoning

For normalized sinc, ∫_{−∞}^{∞}sinc²(x)dx=1. With u=mx, dx=du/m for positive m, so the integral becomes (1/m)∫sinc²(u)du=1/m. Thus option B is correct.

Calculation / Key Relation

∫sinc²(mx)dx=(1/m)∫sinc²(u)du=1/m

Exam Takeaway

Horizontal compression by m reduces area by 1/m.

Common Mistake

Do not multiply the area by m when the x-axis is compressed by m.