Cho hàm số f(x) = x^2 + x - 2 , x lớn hơn bằng 2 và 1/2 x + 3 , x bé hơn 2

a.            \[\int\limits_2^3 {f(x)dx = \int\limits_2^3 {({x^2} + x - 2)dx} } \]  (do \[x \ge 2 \Rightarrow f(x) = {x^2} + x - 2\])

Đúng

b.           \[\int\limits_2^3 {f(x)dx = \int\limits_2^3 {({x^2} + x - 2)dx} }  = \left. {(\frac{1}{3}{x^3} + \frac{1}{2}{x^2} - 2x)} \right|_2^3 = \frac{{15}}{2} - \frac{2}{3} = \frac{{41}}{6}\]

Sai

c.            \[\int\limits_0^1 {f(x)dx = \int\limits_0^1 {(\frac{1}{2}x + 3)dx} }  = \left. {(\frac{1}{4}{x^2} + 3x)} \right|_0^1 = \frac{{13}}{4} - 0 = \frac{{13}}{4}\]

Đúng

d.           \[\int\limits_{ - 1}^3 {f(x)dx = \int\limits_{ - 1}^2 {(\frac{1}{2}x + 3)dx} }  + \int\limits_2^3 {({x^2} + x - 2)dx}  = \frac{{39}}{4} + \frac{{41}}{6} = \frac{{199}}{{12}}\]

Sai