НГ
Николай Гуляев
1)y(x)= ∫xdx=(x^2)/2+c
2) dy(x)/dx=-4x
y(x)= ∫-4xdx=-2(x^2)+c
3)
y(x)= ∫(-3x+2)dx=-3(x^2)/2+2x+c
4)
y(x)= ∫2/(3 ³√x)dx=x ^(2/3)+c
5) x(t)= ∫(2t^2+3t+5)dt=(t^4)/2+(3t^2)/2+5t+c
6) s(t)= ∫4cos(t)dt=4sin(t)+c
7)
y(x)= ∫x+sin(x)dx=(x^2)/2+cos(x)+c
y(x)= ∫Edx=1/(3*E)+c
9)
y(x)= ∫4/(x^3)dx=-2/(x^2)+c
y(1)=2 ; -2+c=2 c=4
y(x)= -2/(x^2)+4
10)
9)
s(t)= ∫8t^3-t^2/2+3dx=2t^4-t^3/9+3t+c
s(0=2 -> c=2
s(t)= 2t^4-t^3/9+3t+2