Let I n = ∫ 0 1 ( 1 − x 2 ) n d x . Which statements are true?

Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationReduction formulaMedium2 minQB

MathematicsMediummultiple choice

Let $I_{n} = \int_{0}^{1} (1 - x^{2})^{n} d x$ . Which statements are true?

Answer:

A, B, C

Solution:

Integration by parts gives $(2 n + 1) I_{n} = 2 n I_{n - 1}$ . Iteration from $I_{0} = 1$ gives both displayed product forms in (B) and (C).

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Reduction formula

⏱ 2mℹ️ Source: QB

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