JEE Main 202624 Jan, Morning shiftMathematicsEasyIntegral Calculus369× since 2002Let f(t)=∫(1−sin(loget)1−cos(loget))dtf(t) = \int \left(\frac{1 - \sin(\log_e t)}{1 - \cos(\log_e t)}\right)dtf(t)=∫(1−cos(loget)1−sin(loget))dt, t>1t > 1t>1. If f(eπ/2)=−eπ/2f\left(e^{\pi/2}\right) = -e^{\pi/2}f(eπ/2)=−eπ/2 and f(eπ/4)=αeπ/4f\left(e^{\pi/4}\right) = \alpha e^{\pi/4}f(eπ/4)=αeπ/4, then α\alphaα equalsAOption A. −1−22-1 - 2\sqrt{2}−1−22BOption B. 1+21 + \sqrt{2}1+2COption C. −1−2-1 - \sqrt{2}−1−2DOption D. −1+2-1 + \sqrt{2}−1+2CheckSkip · show solution
