Question

Спасибо заранее 2-3 задания кому не сложно

Answer 1

$\displaystyle\\1) 2\cos^2(x)+\cos(x)-1=0\\\\\\t=\cos(x)\\\\2t^2+t-1=0\\\\t_1=-1\\t_2=\frac{1}{2}\\\\\left[ \begin{gathered} \ \cos(x)=-1\\\cos(x)=\frac{1}{2} \end{gathered} \right.\\\\\\\left[ \begin{gathered} x=\pi+2\pi k \\ \ x=\pm\frac{\pi}{3}+2\pi n \\ \end{gathered} \right.\\\\\\n,k\in Z$

$\displaystyle\\ 2)\int\limits^1_{-1} {5-x-3x^2} \, dx =(5x-\frac{x^2}{2}-x^3)\mid^1_{-1}=5*1-\frac{1}{2}-1-(5*(-1)-\frac{1}{2}+\\\\\\+1)=5-\frac{1}{2}-1-(-5-\frac{1}{2}+1)=4-\frac{1}{2}-(-4-\frac{1}{2})=4-\frac{1}{2}+4+\frac{1}{2}=\\\\\\=8$