What is the integral from 0 to pi/7 of sec(x)tan(x) ?

The integral from 0 to pi/7 of sec(x)tan(x) is sec(pi/7)-1

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integral from 0 to pi/7 of sec(x)tan(x)

\int_{0}^{\frac{π}{7}} sec (x) tan (x) d x

sec (\frac{π}{7}) - 1

Decimal Notation

0.10991 \dots

Solution steps

\int_{0}^{\frac{π}{7}} sec (x) tan (x) d x

Apply u-substitution

: \int_{1}^{s e c (\frac{π}{7})} 1 d u

= \int_{1}^{s e c (\frac{π}{7})} 1 d u

Integral of a constant:

\int a d x = a x

= [1 \cdot u]_{1}^{s e c (\frac{π}{7})}

Simplify

= [u]_{1}^{s e c (\frac{π}{7})}

Compute the boundaries:

sec (\frac{π}{7}) - 1

= sec (\frac{π}{7}) - 1

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What is the integral from 0 to pi/7 of sec(x)tan(x) ?
The integral from 0 to pi/7 of sec(x)tan(x) is sec(pi/7)-1