Problem
Evaluate the integral. \[ \int_{0}^{\pi / 6} 3 \sec ^{2} x d x \] \[ \int_{0}^{\pi / 6} 3 \sec ^{2} x d x=\square \text { (Type an exact answer, using radicals as needed.) } \]
Solution
Step 1 ：The integral of \(\sec^2(x)\) is \(\tan(x)\). Therefore, the integral of \(3 \sec^2(x)\) is \(3 \tan(x)\). We need to evaluate this from 0 to \(\pi/6\).
Step 2 ：The integral is approximately 1.7320508075688772.
Step 3 ：The final answer is \(\boxed{\sqrt{3}}\).
