1) F'(x) =(3x+sinx -e^2x) ' =(3x)' +(sinx)' -(e^2x) ' =3(x)' +cosx -e^2x*(2x)'
=3 +cosx - 2e^2x*(x) ' = 3 +cosx - 2e^2x*1 = 3 +cosx - 2e^2x.
------------------------------------------------------------------------------------------------------------------
2).F(x) =интеграл(2√xdx)= 2*.интеграл(√xdx) =2*(x)^(1/2+1)/(1/2+1) +C =4/3*x^(4/3) +C.
F(x) =4/3*x^(4/3) +C.
F(0) =7/8 ;
7/8 =4/3*0^(4/3) +C ⇒C =7/8.
F(x) =4/3*x^(4/3) +7/8.
------------------------------------------------------------------------------------------------------------------
S =интеграл(1-->2)(x² -2x+2) =(x³/3 -x² +2x)|1-->2 =(2³/3 -2²+2*2) -(1³/3 -1² +2*1) =4/3.