What is the integral from pi/2 to pi of sec(x)tan(x) ?

The integral from pi/2 to pi of sec(x)tan(x) is diverges

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integral from pi/2 to pi of sec(x)tan(x)

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

diverges

Solution steps

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

Rewrite using trig identities

= \int_{\frac{π}{2}}^{π} \frac{sin ( x )}{cos ^{2} ( x )} d x

Apply u-substitution

: \int_{0}^{- 1} - \frac{1}{u ^{2}} d u

= \int_{0}^{- 1} - \frac{1}{u ^{2}} d u

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

= - \int_{- 1}^{0} - \frac{1}{u ^{2}} d u

Take the constant out:

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

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

Apply the Power Rule

: [- \frac{1}{u}]_{- 1}^{0}

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

Simplify

= [- \frac{1}{u}]_{- 1}^{0}

Compute the boundaries:

diverges

= diverges

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What is the integral from pi/2 to pi of sec(x)tan(x) ?
The integral from pi/2 to pi of sec(x)tan(x) is diverges