CBSE Boardहिन्दी माध्यमकक्षा 12 साइन्सगणितसमाकलन1 Mark
MCQ
$\int_0^{\pi / 4} \tan ^2 x d x$ का मान है$-$
✓
$1-\frac{\pi}{4}$
B
$1+\frac{\pi}{4}$
C
$-1+\frac{\pi}{4}$
D
$-1-\frac{\pi}{4}$
✓
Answer
Correct option: A.
$1-\frac{\pi}{4}$
$ \int_0^{\pi / 4} \tan ^2 x d x =\int_0^{\pi / 4}\left(\sec ^2 x-1\right) d x$
$ =\int_0^{\pi / 4} \sec ^2 x d x-\int_0^{\pi / 4} d x$
$ =[\tan x]_0^{\frac{\pi}{4}}-[x]_0^{\frac{\pi}{4}}$
$ =\left(\tan \frac{\pi}{4}-\tan 0\right)-\left(\frac{\pi}{4}-0\right)$
$ =\left(\tan \frac{\pi}{4}-0-\frac{\pi}{4}\right)=1-\frac{\pi}{4}$
अत: सही विकल्प $A$ है ।
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.