Ответ:
Пошаговое объяснение:
а) ∫₁²dx/√(5x-1) = |пусть 5х-1=t, 5dx=dt, dx=dt/5 |
=1/5∫dt/√t= 2/5 · √t =2/5·√(5x-1) |₁²=2/5 · (10-1 -5+1)=2/5 ·5 = 2
б)∫₀²ⁿ⁾³ Cos(x/2)dx = |пусть х/2=t, 1/2 · dx=dt, dx=2dt | =2∫Cost dt = 2Sint= 2Sin (x/2) |₀²ⁿ⁾³ = 2·(Sin π/3 - Sin0)=2·(√3/2)=√3
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Ответ:
Пошаговое объяснение:
а) ∫₁²dx/√(5x-1) = |пусть 5х-1=t, 5dx=dt, dx=dt/5 |
=1/5∫dt/√t= 2/5 · √t =2/5·√(5x-1) |₁²=2/5 · (10-1 -5+1)=2/5 ·5 = 2
б)∫₀²ⁿ⁾³ Cos(x/2)dx = |пусть х/2=t, 1/2 · dx=dt, dx=2dt | =2∫Cost dt = 2Sint= 2Sin (x/2) |₀²ⁿ⁾³ = 2·(Sin π/3 - Sin0)=2·(√3/2)=√3