Question

Помогите решить очень надо.

Answer 1

1)=7x³/15 |(от1 до 2)=7/15(8-1)=7/15*7=49/15
2)=2/5*√(5х-1)| (от 1 до 2)=2/5*(√9-√4)=2/5*(3-2)=2/5
3)S=$intlimits {(1/2x^2+1)} , dx$=x³/6+x|(от -2 до 3)=27/6+3+8/6+2=
=5+35/6=5+5 5/6=10 5/6

Answer 2

$int _1^2, frac{7}{5}x^2cdot dx=frac{7}{5}cdot frac{x^3}{3}|_1^2=frac{7}{15}(2^3-1^3)=frac{49}{15}\\\int _1^2, frac{dx}{sqrt{5x-1}}=[t=5x-1,dt=5dx,to dx=frac{dt}{5}]=frac{1}{5}int _4^9frac{dt}{sqrt{t}}=\\=frac{1}{5}cdot 2sqrt{t}, |_4^9=frac{2}{5}cdot (sqrt9-sqrt4)=frac{2}{5}cdot (3-2)=frac{2}{5}\\\S=int_{-2}^3(frac{1}{2}x^2+1)dx=(frac{1}{2}cdot frac{x^3}{3}+x)|_{-2}^3=frac{1}{2}cdot frac{3^3}{3}+3-(frac{1}{2}cdot frac{(-2)^3}{3}-2)=$

$=frac{9}{2}+3+frac{4}{3}+2=5+frac{35}{6}=10frac{5}{6}$