What is the integral from 0 to pi/(20) of tan(10x) ?

The integral from 0 to pi/(20) of tan(10x) is diverges

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integral from 0 to pi/(20) of tan(10x)

\int_{0}^{\frac{π}{20}} tan (10 x) d x

diverges

Solution steps

\int_{0}^{\frac{π}{20}} tan (10 x) d x

Rewrite using trig identities

= \int_{0}^{\frac{π}{20}} \frac{sin ( 10 x )}{cos ( 10 x )} d x

Apply u-substitution

= \int_{1}^{0} - \frac{1}{10 u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{0}^{1} - \frac{1}{10 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - (- \frac{1}{10} \cdot \int_{0}^{1} \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- \frac{1}{10} [ln ∣ u ∣]_{0}^{1})

Simplify

= \frac{1}{10} [ln ∣ u ∣]_{0}^{1}

Compute the boundaries:

diverges

= diverges

d er i v a t i v e f (x) = (2 x - 3) \cdot x

\frac{d}{d x} (2 sin (x))

t an g e n t \frac{2}{1 - t}, at t = - 2

t a y l or f (x) = 3 0^{3} - 3 x^{2} + 12 x - 74

\frac{d}{d x} (6 e^{- 2 x})

What is the integral from 0 to pi/(20) of tan(10x) ?
The integral from 0 to pi/(20) of tan(10x) is diverges