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Maths Definite Integral and Area Under Curves General Subjective Type

Published on: August 12, 2026

If φ (x) = cos x – , then prove that

φ′′ (x) + φ (x) = –cos x.

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Sol. We have,

φ (x) = cos x –

By using Lebnitz's rule, we get

φ′ (x) = –sin x –

= – sin x –

Differentiating both sides w.r. to x, we get

φ′′ (x) = –cos x – φ (x)

⇒ φ′′ (x) + φ (x) = –cos x

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