Tính các tích phân sau: a) tích phân 0 1 (1-2x)^2dx; b) tích phân 1 4 (x - 2) / căn 2dx}.

a) \(\int\limits_0^1 {{{\left( {1 - 2x} \right)}^2}} dx\) = \(\int\limits_0^1 {\left( {1 - 4x + 4{x^2}} \right)} dx\)

                          = \(\left. {\left( {x - 2{x^2} + \frac{4}{3}{x^3}} \right)} \right|_0^1\)

                          = \(\frac{1}{3}\).

b) \(\int\limits_1^4 {\frac{{x - 2}}{{\sqrt x }}dx} \) = \(\int\limits_1^4 {\left( {\sqrt x  - \frac{2}{{\sqrt x }}} \right)dx} \)

                      = \(\int\limits_1^4 {\left( {\sqrt x  - 2.{x^{\frac{{ - 1}}{2}}}} \right)dx} \)

                      = \(\left. {\left( {\frac{2}{3}x\sqrt x  - 4\sqrt x } \right)} \right|_1^4\)

                      = \(\frac{2}{3}\).