Задача 74663 ...

6575ed29e2fb170457c22c98

12/10/2023 4:55:40 PM

∫ sin^3x*cosx dx от 0 до Pi/4

626fab9a354ab65fb2f43abb

12/10/2023 5:55:13 PM

★

[m]\int_{0}^{\pi/4} \sin^3\ x \cdot \cos\ x\ dx[/m]
Замена sin x = y; dy = (sin x)' = cos x dx
Пределы интегрирования: y(0) = 0; y(π/4) = sqrt(2)/2
[m]\int_{0}^{\sqrt{2}/2} y^3\ dy = \frac{y^4}{4}|_{0}^{\sqrt{2}/2} = \frac{2^2}{2^4 \cdot 4} - 0 = \frac{4}{64} = \frac{1}{16}[/m]