Question

Сегодня: вычислить определённый интеграл: интеграл пи\6 от пи\4; tg^2 xdx.

Answer 1

$\int\limits^{\frac{\pi}{4}}_{\frac{\pi}{6}} {tn^2x} \, dx = \int\limits^{\frac{\pi}{4}}_{\frac{\pi}{6}} {\frac{sin^2x}{cos^2x}} \ dx = \int\limits^{\frac{\pi}{4}}_{\frac{\pi}{6}} {\frac{1-cos^2x}{cos^2x}} \ dx = \int\limits^{\frac{\pi}{4}}_{\frac{\pi}{6}} {(\frac{1}{cos^2x}-1)} \ dx = \int\limits^{\frac{\pi}{4}}_{\frac{\pi}{6}} {\frac{1}{cos^2x}} \ dx + \int\limits^{\frac{\pi}{4}}_{\frac{\pi}{6}} {(-1)} \ dx =tnx - x$