Match List I to List II. (P) Number of solutions of ⌊ x ⌋ = ∣2 x − 1∣ . (Q) If ∫ 0 2 π 1 + t a n 4 x d x = π / k , find k . (R) ∫ 0 ∞ 1 + x 2 l n x d x . (S) If y = sin − 1 ( cos ( sin − 1 x )

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Match List I to List II. (P) Number of solutions of ⌊ x ⌋ = ∣2 x − 1∣ . (Q) If ∫ 0 2 π ​ 1 + t a n 4 x d x ​ = π / k , find k . (R) ∫ 0 ∞ ​ 1 + x 2 l n x ​ d x . (S) If y = sin − 1 ( cos ( sin − 1 x ) ) + cos − 1 ( sin ( cos − 1 x ) ) , find d y / d x at x = π /6 . List II: (1) 1, (2) 0, (3) 3, (4) 2.

TestHub · Accepted Answer

(P) The solutions are x = 1/2 and x = 1 , so P-4. (Q) Symmetry gives the integral π , hence k = 1 , so Q-1. (R) Substitution x ↦ 1/ x negates the integral, so it is 0 , R-2. (S) The expression is locally constant after principal-value simplification, so the derivative is 0, S-2.

Mathematics - Indefinite Integration Question with Solution | TestHub

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