Question

математика помогите!!!

Answer 1

a)
$y=-x^{2}+4x y=0 x=2 \ -x^{2}+4x=0 \ -x(x-4)=0 \ x=0 x= 4 \ S=int limits^0_2(-x^{2}+4x)dx = mid^0_2(-frac{x^{3}}{3}+2x^{2}) \ -frac{8}{3}+8=-frac{16}{3}$


b)
$y=cosx \ y=0 x=-frac{pi}{6} x=frac{pi}{6} \ S=int limits^frac{-pi}{6}_frac{pi}{6}(cosx)dx \ mid^frac{-pi}{6}_frac{pi}{6}(-sinx)=mid^frac{5pi}{6}_frac{pi}{6}-sinx \ -frac{1}{2}-frac{1}{2}=-1$


v)
$y=x^{2} y=x+2 \ x^{2}=x+2 \ x^{2}-x-2=0 \ x_{1}=2 x_{2}=-1 \ S=intlimits^2_1=mid^1_2 frac{x^{2}}{2}+2x=frac{-3}{2}+6=-frac{15}{2} \ S=-3+frac{15}{2}=frac{9}{2}$