Evaluate the integral.
$\int_{0}^{π / 6} 3 \sec^{2} x d x$

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Answer

Final Answer: $\sqrt{3}$

Steps

Step 1 ：The integral of $\sec^{2} (x)$ is $\tan (x)$ . Therefore, the integral of $3 \sec^{2} (x)$ is $3 \tan (x)$ .

Step 2 ：We need to evaluate this from 0 to $\frac{π}{6}$ .

Step 3 ：The integral of $3 \sec^{2} (x)$ from 0 to $\frac{π}{6}$ is $\sqrt{3}$ .

Step 4 ：Final Answer: $\sqrt{3}$