pi-4-pi-4-dx-cos-2-x-9-7-tan-x-dx-

Question Number 166263 by cortano1 last updated on 17/Feb/22

\int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{dx}{\cos^{2} x \sqrt{9 + 7 \tan ∣ x ∣}} dx = ?

Answered by mathsmine last updated on 17/Feb/22

= 2 \int_{0}^{\frac{π}{4}} \frac{d x}{{c o s}^{2} (x) \sqrt{9 + 7 t g (x)}}

= 2 \int_{0}^{1} \frac{d u}{\sqrt{9 + 7 u}} = \frac{4}{7} ({[\sqrt{9 + 7 u}]}_{0}^{1})

= \frac{4}{7}