Cho \(\int\limits_{0}^{2}{f\left( x \right)\text{d}x=5}\). Tính tích phân \(I=\int\limits_{0}^{2}{\left[ {{x}^{2}}+2f\left( x \right) \right]\text{d}x}\).

* Hướng dẫn giải

\(I = \int\limits_0^2 {\left[ {{x^2} + 2f\left( x \right)} \right]{\rm{d}}x}  = \int\limits_0^2 {{x^2}{\rm{d}}x + 2\int\limits_0^2 {f\left( x \right){\rm{d}}x} }  = \frac{8}{3} + 2.5 = \frac{{38}}{3}\)