What is the integral from (-pi)/4 to pi/4 of tan(x) ?

The integral from (-pi)/4 to pi/4 of tan(x) is 0

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integral from (-pi)/4 to pi/4 of tan(x)

\int_{\frac{- π}{4}}^{\frac{π}{4}} tan (x) d x

0

Solution steps

\int_{\frac{- π}{4}}^{\frac{π}{4}} tan (x) d x

Rewrite using trig identities

= \int_{\frac{- π}{4}}^{\frac{π}{4}} sin (x) sec (x) d x

Apply Integration By Parts

= [- \int - tan (x) d x - 1]_{- \frac{π}{4}}^{\frac{π}{4}}

\int - tan (x) d x = ln ∣ cos (x) ∣

= [- ln ∣ cos (x) ∣ - 1]_{- \frac{π}{4}}^{\frac{π}{4}}

Compute the boundaries:

0

= 0

What is the integral from (-pi)/4 to pi/4 of tan(x) ?
The integral from (-pi)/4 to pi/4 of tan(x) is 0