What is the integral from pi/6 to pi/3 of sec^2(x) ?

The integral from pi/6 to pi/3 of sec^2(x) is sqrt(3)-1/(sqrt(3))

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integral from pi/6 to pi/3 of sec^2(x)

\int_{\frac{π}{6}}^{\frac{π}{3}} sec^{2} (x) d x

3 - \frac{1}{3}

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{3}} sec^{2} (x) d x

Use the common integral:

\int sec^{2} (x) d x = tan (x)

= [tan (x)]_{\frac{π}{6}}^{\frac{π}{3}}

Compute the boundaries:

3 - \frac{1}{3}

= 3 - \frac{1}{3}

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What is the integral from pi/6 to pi/3 of sec^2(x) ?
The integral from pi/6 to pi/3 of sec^2(x) is sqrt(3)-1/(sqrt(3))