Cho \(\int\limits_0^2 {f\left( x \right)dx} = 3,\int\limits_0^3 {f\left( x \right)dx = 5} \). Xét tính đúng sai của các khẳng định sau:

a) S, b) Đ, c) Đ, d) S

a) \(\int\limits_2^0 {f\left( x \right)dx = - \int\limits_0^2 {f\left( x \right)dx = - 3} } \).

b) Ta có \(\int\limits_0^3 {f\left( x \right)dx = } \int\limits_0^2 {f\left( x \right)dx} + \int\limits_2^3 {f\left( x \right)dx} \)\( \Rightarrow \int\limits_2^3 {f\left( x \right)dx} = \int\limits_0^3 {f\left( x \right)dx - } \int\limits_0^2 {f\left( x \right)dx} = 5 - 3 = 2\).

c) \(\int\limits_0^2 {\left( {f\left( x \right) - 2x} \right)dx = \int\limits_0^2 {f\left( x \right)dx} - \int\limits_0^2 {2xdx = } 3 - \left. {{x^2}} \right|_0^2} = 3 - 4 = - 1\).

d) \(\int\limits_0^2 {f\left( {\frac{x}{3}} \right)dx} \)\( = 3\int\limits_0^2 {f\left( {\frac{x}{3}} \right)d\left( {\frac{x}{3}} \right)} \)\( = 3\int\limits_0^2 {f\left( t \right)dt} = 3.3 = 9\).