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

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

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

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

\frac{2}{3}

Decimal

1.15470 \dots

Solution steps

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

Use the common integral:

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

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

Compute the boundaries:

\frac{2}{3}

= \frac{2}{3}

\int_{0}^{1} (x + y + z) d x

\int_{0}^{2} \frac{1}{( 1 - x ^{2} )} d x

\int_{1}^{2} x e^{- 2 x^{2}} d x

\int_{- 2}^{0} - x d x

\int_{0}^{5} 2 x^{2} d x

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