Let f(t)=\int (\frac{1- \sin (\log _e t) }{1-\cos (\log _e t) }) \dt, t1. If f (e^{\pi \/ 2}) =-e^{\pi \/ 2} and f (e^{\pi \/ 4}) =\alpha e^{\pi \/ 4}, then \alpha equals [24 jan 2026 Shift 1]

Question

Let f(t)=\int (\frac{1- \sin (\log _e t) }{1-\cos (\log _e t) }) \dt, t>1. If f (e^{\pi \/ 2}) =-e^{\pi \/ 2} and f (e^{\pi \/ 4}) =\alpha e^{\pi \/ 4}, then \alpha equals [24 jan 2026 Shift 1]

Examsnet · Accepted Answer

Correct Answer is : −1−√2

Indefinite Integrals