Let I ( n ) = ∫ 0 π ( 1 − ∣ sin x ∣ + ∣ sin 2 x ∣ − ∣ sin 3 x ∣ + ⋯ up to n terms ) d x . Which are true?

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Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationProperties of definite integrationEasy2 minQB

MathematicsEasymultiple choice

Let $I (n) = \int_{0}^{π} (1 - ∣ sin x ∣ + ∣ sin 2 x ∣ - ∣ sin 3 x ∣ + \dots$ up to $n$ terms $) d x$ . Which are true?

Options:(select one or more)

Answer:

A, B, C, D

Solution:

For every positive integer $m, \int_{0}^{π} ∣ sin m x ∣ d x = 2$ . The alternating sum therefore equals $π - 2$ for even $n$ and $π$ for odd $n$ , proving all statements.

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Properties of definite integration

⏱ 2mℹ️ Source: QB

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