Given below are two statements. Statement - 1: _ 0 ^ + y | x| d x=2 n+1- v where त E E…
Mathematics · JEE Main · NTA Exams — Integral Calculus
Given below are two statements.
Statement - 1: \(\int_{0}^{\pi+\mathrm{y}}|\sin x| d x=2 n+1-\cos v\) where \(\text { त E E }\) and \(0 \leq v<\pi\).
Statement - 2: If f(x) is a periodic function with period T, then
- \(\int_{0}^{\pi T} f(x) d x=n \int_{0}^{T} f(x) d x\), where n ∈ N and
- \(\int_{\pi T}^{\pi T+a} f(x) d x=\int_{a}^{a} f(x) d x .\) where n ∈ N.
In the light of the above statements, choose the correct answer from the options given below:
- Both Statements are true and Statement - 2 is the correct explanation for Statement - 1
- Both Statements are true and Statement - 2 is not a correct explanation for Statement - 1
- Statement - 1 is true and Statement - 2 is false
- Statement - 1 is false and Statement - 2 is true
Answer
(C) Statement - 1 is true and Statement - 2 is false
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