What is the integral from-pi/4 to pi/4 of tan^2(x) ?

The integral from-pi/4 to pi/4 of tan^2(x) is -pi/2+2

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integral from-pi/4 to pi/4 of tan^2(x)

\int_{- \frac{π}{4}}^{\frac{π}{4}} tan^{2} (x) d x

- \frac{π}{2} + 2

Solution steps

\int_{- \frac{π}{4}}^{\frac{π}{4}} tan^{2} (x) d x

Rewrite using trig identities

= \int_{- \frac{π}{4}}^{\frac{π}{4}} - 1 + sec^{2} (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{- \frac{π}{4}}^{\frac{π}{4}} 1 d x + \int_{- \frac{π}{4}}^{\frac{π}{4}} sec^{2} (x) d x

\int_{- \frac{π}{4}}^{\frac{π}{4}} 1 d x = \frac{π}{2}

\int_{- \frac{π}{4}}^{\frac{π}{4}} sec^{2} (x) d x = 2

= - \frac{π}{2} + 2

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What is the integral from-pi/4 to pi/4 of tan^2(x) ?
The integral from-pi/4 to pi/4 of tan^2(x) is -pi/2+2