a) Diện tích cần tính là:

S = \(\int\limits_0^5 {\left| {{x^2} - 4} \right|dx}  = \int\limits_0^2 {\left| {{x^2} - 4} \right|dx}  + \int\limits_2^5 {\left| {{x^2} - 4} \right|dx} \)

                         = \(\int\limits_0^2 {\left( {4 - {x^2}} \right)dx}  + \int\limits_2^5 {\left( {{x^2} - 4} \right)dx} \)

                         = \(\left. {\left( {4x - \frac{{{x^3}}}{3}} \right)} \right|_0^2 + \left. {\left( {\frac{{{x^3}}}{3} - 4x} \right)} \right|_2^5\)

                         = 4.2 – \(\frac{8}{3}\) − 4.0 + \(\frac{0}{3}\) + \(\frac{{{5^3}}}{3}\) − 4.5 – \(\frac{8}{3}\) + 4.2 = \(\frac{{97}}{3}\).

b) Diện tích cần tính là:

S = \(\int\limits_0^2 {\left| { - {x^2} + 9 - \left( {2x + 1} \right)} \right|dx} \) = \(\int\limits_0^2 {\left| { - {x^2} - 2x + 8} \right|} dx\)

                                         = \(\int\limits_0^2 {\left( { - {x^2} - 2x + 8} \right)dx} \)

                                         = \(\left. {\left( {\frac{{ - {x^3}}}{3} - {x^2} + 8x} \right)} \right|_0^2\) = \(\frac{{28}}{3}\).