_ - 4 ^ 4 ^2x dx is equal to: 1. -1 2. 0 3. 1 4. 2 - Vidyadip

Question

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

-1
0
1
2

✓

Answer

2

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

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