Question

Вычислите интеграл
[п/4;0] ∫ 2sin4x dx

Answer 1

$displaystyle intlimits^big{frac{pi}{4}}_02sin4x,dx=2cdotbigg(-dfrac{cos4x}{4}bigg)bigg|^big{frac{pi}{4}}_0=-dfrac{cos4x}{2}bigg|^big{frac{pi}{4}}_0=-dfrac{cos(4cdotfrac{pi}{4})}{2}-\ \ \ -bigg(-dfrac{cos(4cdot0)}{2}bigg)=-dfrac{overbrace{cospi}^{-1}}{2}+dfrac{overbrace{cos0}^{1}}{2}=dfrac{1}{2}+dfrac{1}{2}=1$