y=3x^2+1,y=3x+7
3x^2+1=3x+7
3x^2–3x–6=0
x^2–x–2=0
D=9
x_(1)=–1; x_(2)=2
V=π ∫ ^(2)_(-1) ((3x+7)^2-(3x^2+1)^2)dx=
=π ∫ ^(2)_(-1) (9x^2+42x+49-9x^4-6x^2-1)dx=
=π ∫ ^(2)_(-1) (3x^2+42x+48-9x^4)dx=
=π*(x^3+21x^2+48x-(9x^5/5))|^(2)_(-1)=
=π*(2^3-(-1)^3+21*(4-1)+48(2-(-1))-(9/5)*(32-(-1)))=
=π*(9+63+144-(297/5))= [b]π*(183/5)[/b]