a) S, b) Đ, c) Đ, d) S

a) \({S_1} = \int\limits_0^3 {\left| { - {x^2} + 4x - x} \right|} dx\)\( = \int\limits_0^3 {\left| { - {x^2} + 3x} \right|} dx\).

b) \({S_2} = \int\limits_0^4 {\left| {{x^2} - 4x} \right|dx} - {S_1}\).

c) \({S_2} = \int\limits_3^4 {\left| { - {x^2} + 4x} \right|dx} + {S_{\Delta OAB}} = \int\limits_3^4 {\left( { - {x^2} + 4x} \right)dx} + \frac{1}{2}.3.3 = \int\limits_3^4 {\left( { - {x^2} + 4x} \right)dx} + \frac{9}{2}\).

(với \(A\left( {3;0} \right),B\left( {3;3} \right)\)).

d) \(V = \pi \int\limits_0^3 {{x^2}dx} + \pi \int\limits_3^4 {{{\left( { - {x^2} + 4x} \right)}^2}dx} = 9\pi + \frac{{53\pi }} = \frac{{188\pi }} > 30\).