Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
If $\int_{\log 2}^a \frac{ e ^x}{\sqrt{ e ^x-1}} d x=2$, then $a =$
A
$0$
B
2 log 2
✓
log 5
D
log 2
✓
Answer
Correct option: C.
log 5
(C) $\int_{\log 2}^{ a } \frac{ e ^x}{\sqrt{ e ^x-1}} d x=2$ Put $e ^x-1= t \Rightarrow e ^x d x= dt$ $\therefore \quad \int_1^{ e ^{ a }-1} \frac{ dt }{\sqrt{ t }}=2$ $\Rightarrow[2 \sqrt{ t }]_1^{ e ^{ a }-1}=2$ $\Rightarrow \sqrt{ e ^{ a }-1}-1=1$ $\Rightarrow \sqrt{ e ^{ a }-1}=2$ $\Rightarrow e ^{ a }-1=4$ $\Rightarrow e ^{ a }=5$ $\Rightarrow a =\log 5$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.