_ - 4 ^ 4 ^2x dx is equal to: - Vidyadip

MCQ

$\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sec^2\text{x dx}$ is equal to:

A
$-1$
B
$0$
C
$1$
✓
$2$

✓

Answer

Correct option: D.

$2$

$\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sec^2\text{x dx}$
$\Rightarrow\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sec^2\text{x dx}=\Big[\tan\text{x}\Big]^{\frac{\pi}{4}}_{-\frac{\pi}{4}}$
$\Rightarrow\Big[\tan\big(\frac{\pi}{4}\big)-\tan\big(-\frac{\pi}{4}\big)\Big]$
$\Rightarrow[1-(-1)]$
$\Rightarrow2$

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