Search any question & find its solution
Question:
Answered & Verified by Expert
If $\mathrm{I}=\int_0^{\mathrm{I}} \frac{\mathrm{dx}}{1+\mathrm{x}^{\pi / 2}}$, then
Options:
Solution:
1100 Upvotes
Verified Answer
The correct answer is:
$\log _{\mathrm{e}} 2 < 1 < \pi / 4$
Hints: $\mathrm{x}^2 < \mathrm{x}^{\frac{\pi}{2}} < \mathrm{x}, \quad 1+\mathrm{x}^2 < 1+\mathrm{x}^{\frac{\pi}{2}} < 1+\mathrm{x}$
$\frac{1}{1+x^2}>\frac{1}{1+x^{\frac{\pi}{2}}}>\frac{1}{1+x}$
$\frac{\pi}{4}>\mathrm{I}>(\log (1+\mathrm{x})), \quad \frac{\pi}{4}>\mathrm{I}>\log 2$
$\frac{1}{1+x^2}>\frac{1}{1+x^{\frac{\pi}{2}}}>\frac{1}{1+x}$
$\frac{\pi}{4}>\mathrm{I}>(\log (1+\mathrm{x})), \quad \frac{\pi}{4}>\mathrm{I}>\log 2$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.