Question
$\int\limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sec^2\text{x dx}$ is equal to:
  1. -1
  2. 0
  3. 1
  4. 2

Answer

  1. 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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