Given below are two statements. Let I_ n = _ 0 ^ / 4 ^ n x d x Statement - 1: 1 n+1…
Mathematics · JEE Main · NTA Exams — Integral Calculus
Given below are two statements.
Let \(I_{n}=\int_{0}^{\pi / 4} \tan ^{n} x d x\)
Statement - 1: \(\frac{1}{n+1}<2 I_{n}<\frac{1}{n-1}\) for all n = 2, 3, 4, ...
Statement - 2: \(I_{n}+I_{n-2}=\frac{1}{n-1}, n=3,4,5, \ldots\)
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
(A) Both Statements are true and Statement - 2 is the correct explanation for Statement - 1
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