Let f(x) be a non-negative continuous function such that the area bounded by the curve y…
Mathematics · JEE Main · NTA Exams — Integral Calculus
Let f(x) be a non-negative continuous function such that the area bounded by the curve y = f(x), x-axis and the ordinates \(x=\frac{\pi}{4} \text { and } x=\beta>\frac{\pi}{4}\) \(\text { is }\left(\beta \sin \beta+\frac{\pi}{4} \cos \beta+\sqrt{2} \beta\right) .\)
Then \(f\left(\frac{\pi}{2}\right)\) is,
- \(\left(\frac{\pi}{4}-\sqrt{2}+1\right)\)
- \(\left(\frac{\pi}{4}+\sqrt{2}-1\right)\)
- \(\left(1-\frac{\pi}{4}+\sqrt{2}\right)\)
- \(\left(1-\frac{\pi}{4}-\sqrt{2}\right)\)
Answer
(B) ( 4 + 2 -1 )
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