Задача 38148 ...

vk503151203

2019-06-14 09:33:28

Вычислите ∫ 6/(cos^22x) dx от n/2 до -n/6

sova

2019-06-14 09:39:21

Табличный интеграл
∫ du/cos^2u=tgu+C

u=2x
d(2x)=2dx⇒ dx=(1/2)d(2x)
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=(1/2)*6 ∫^(π/6)_(-π/6) d( [b]2x[/b])/cos^2( [b]2x[/b])=

=3*(tg(2x))|^(π/6)_(-π/6)=

=3*(tg(π/3)-tg(-π/3))=3*(sqrt(3)-(-sqrt(3))=3*2sqrt(3)= [b]6sqrt(3)[/b]