What is the integral from 0 to pi/6 of (sec(x)tan(x)) ?

The integral from 0 to pi/6 of (sec(x)tan(x)) is 2/(sqrt(3))-1

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integral from 0 to pi/6 of (sec(x)tan(x))

\int_{0}^{\frac{π}{6}} (sec (x) tan (x)) d x

\frac{2}{3} - 1

Decimal

0.15470 \dots

Solution steps

\int_{0}^{\frac{π}{6}} sec (x) tan (x) d x

Apply u-substitution

= \int_{1}^{\frac{2 3}{3}} 1 d u

Integral of a constant:

\int a d x = a x

= [1 \cdot u]_{1}^{\frac{2 3}{3}}

Simplify

[1 \cdot u]_{1}^{\frac{2 3}{3}} : [u]_{1}^{\frac{2}{3}}

= [u]_{1}^{\frac{2}{3}}

Compute the boundaries:

\frac{2}{3} - 1

= \frac{2}{3} - 1

What is the integral from 0 to pi/6 of (sec(x)tan(x)) ?
The integral from 0 to pi/6 of (sec(x)tan(x)) is 2/(sqrt(3))-1