Далее S означает интеграл, запись [a,b] означает разность F(b)-F(a)
1.
= x^4-x³+x²+x= [x1=-2 x2=3] =81-27+9+3-16-8-4+2=40
2. =S 3x^1/2dx+S4x^-1/2dx=3*2/3*x^3/2 +8√x=2√x³+8√x=... [1,4]=16+16-2-8=22
3. =3sinx+2cosx = [0,π/2] =3sinπ/2+2cosπ/2-3sin0-2cos0=3+0-0-2=1
4. =3tgx [π/6,π/4]=3tgπ/4-3tgπ/6=3-3/√3=3-√3
5. = x³/3-1/3*x^(-3 )= [1,2]=8/3-1/24-1/3+1/3=64/24-1/24=63/24=2.625
6. =-1/2*cos2x [0,π]... = -1/2*cos2π+1/2cos0 =-1/2+1/2=0
7. Sx(3-x)dx=S3xdx-Sx²dx=3/2*x²-1/3*x³= [0,2]... =6-8/3=10/3
F(2)=6-8/3
F(0)=0
8. по таблице основных интегралов S dx/(x²-3²) = -Sdx/(3²-x²)=
=-1/6*ln|(3+x)/(3-x)|
F(1)=-1/6 ln4/2 F(0)=-1/6*ln3/3=0 F(1)-F(0)=-1/6 ln2