Evaluate the integral.
\[
\int_{0}^{\pi / 6} 3 \sec ^{2} x d x
\]
\[
\int_{0}^{\pi / 6} 3 \sec ^{2} x d x=\square \text { (Type an exact answer, using radicals as needed.) }
\]

Answer

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Answer

The final answer is \(\boxed{\sqrt{3}}\).

Steps

Step 1 ：The integral of \(\sec^2(x)\) is \(\tan(x)\). Therefore, the integral of \(3 \sec^2(x)\) is \(3 \tan(x)\). We need to evaluate this from 0 to \(\pi/6\).

Step 2 ：The integral is approximately 1.7320508075688772.

Step 3 ：The final answer is \(\boxed{\sqrt{3}}\).

Evaluate the integral.\[\int_{0}^{\pi / 6} 3 \sec ^{2} x d x\]\[\int_{0}^{\pi / 6} 3 \sec ^{2} x d x=\square \text { (Type an exact answer, using radicals as needed.) }\]

Answer

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Evaluate the integral.
\[
\int_{0}^{\pi / 6} 3 \sec ^{2} x d x
\]
\[
\int_{0}^{\pi / 6} 3 \sec ^{2} x d x=\square \text { (Type an exact answer, using radicals as needed.) }
\]