ln 2
Пошаговое объяснение:
График на рисунке.
Integral (0; π/4) tg x dx + Integral (π/4; π/2) ctg x dx =
= - ln |cos x| |(0; π/4) + ln |sin x| |(π/4; π/2) =
= - ln |cos(π/4)| + ln |cos 0| + ln |sin(π/2)| - ln |sin(π/4)| =
= -ln (1/√2) + ln 1 + ln 1 - ln (1/√2) = -2ln (1/√2) = 2ln (√2) = ln (√2)^2 = ln 2
ln 2
Пошаговое объяснение:
График на рисунке.
Integral (0; π/4) tg x dx + Integral (π/4; π/2) ctg x dx =
= - ln |cos x| |(0; π/4) + ln |sin x| |(π/4; π/2) =
= - ln |cos(π/4)| + ln |cos 0| + ln |sin(π/2)| - ln |sin(π/4)| =
= -ln (1/√2) + ln 1 + ln 1 - ln (1/√2) = -2ln (1/√2) = 2ln (√2) = ln (√2)^2 = ln 2