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Maths Definite Integral and Area Under Curves Integration as a Limit of Sum and Reduction Formula Subjective Type

Published on: August 14, 2026

(i)If Ι n = , then show that Ι n + Ι n – 2 =

(ii) Ι n = . Show that Ι n = Ι n–2 ∀ n ≥ 2

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The correct answer is:

CHECK THE SOLUTION.

(i) Ι n = ⇒ Ι n – 2 =

Ι n + Ι n – 2 = = =

(ii) Ι n = = (sinx) n–1 (cosx) + (n – 1)

⇒ Ι n = (n – 1) ⇒ Ι n = (n – 1) Ι n–2 – (n – 1) Ι n ⇒ Ι n = Ι n–2

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