What is the integral from pi/6 to 1.56 of tan(x) ?

The integral from pi/6 to 1.56 of tan(x) is 4.38472…

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integral from pi/6 to 1.56 of tan(x)

\int_{\frac{π}{6}}^{1.56} tan (x) d x

4.38472 \dots

Solution steps

\int_{\frac{π}{6}}^{1.56} tan (x) d x

Rewrite using trig identities

= \int_{\frac{π}{6}}^{1.56} \frac{sin ( x )}{cos ( x )} d x

Apply u-substitution

: \int_{\frac{3}{2}}^{0.01079 \dots} - \frac{1}{u} d u

= \int_{\frac{3}{2}}^{0.01079 \dots} - \frac{1}{u} d u

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

= - \int_{0.01079 \dots}^{\frac{3}{2}} - \frac{1}{u} d u

Take the constant out:

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

= - (- \int_{0.01079 \dots}^{\frac{3}{2}} \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - (- [ln ∣ u ∣]_{0.01079 \dots}^{\frac{3}{2}})

Simplify

= [ln ∣ u ∣]_{0.01079 \dots}^{\frac{3}{2}}

Compute the boundaries:

4.38472 \dots

= 4.38472 \dots

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What is the integral from pi/6 to 1.56 of tan(x) ?
The integral from pi/6 to 1.56 of tan(x) is 4.38472…