Question

найдите значение параметра а с площадью криволинейной трапеций

Answer 1

$\displaystyle \int\limits^a_0 {(\sin x+\sqrt{3}\cos x)} \, dx =(-\cos x+\sqrt{3}\sin x)|^a_0=\\ \\ =\bigg(2\sin\bigg(x- \frac{\pi}{6}\bigg)\bigg)\bigg|^a_0 =2\sin\bigg(a- \frac{\pi}{6} \bigg)-2\sin\bigg(-\frac{\pi}{6} \bigg)=2\\ \\ \sin\bigg(a-\frac{\pi}{6} \bigg)+0.5=1\\ \\ \\ \sin\bigg(a-\frac{\pi}{6} \bigg)=0.5\\ \\ \\ a-\frac{\pi}{6} =\frac{\pi}{6} \\ \\ \\ a=\frac{\pi}{3}$