Question

So sánh \(\int\limits^1_02xdx+\int\limits^2_12xdx\) và \(\int\limits^2_02xdx\).

Answer 1

\(\int\limits_0^1 {2xdx} + \int\limits_1^2 {2xdx} = \left. {{x^2}} \right|_0^1 + \left. {{x^2}} \right|_1^2 = 1 + 4 - 1 = 4\).

\(\int\limits_0^2 {2xdx} = \left. {{x^2}} \right|_0^2 = 4\).

Vậy \(\int\limits_0^1 {2xdx} + \int\limits_1^2 {2xdx} \) = \(\int\limits_0^2 {2xdx} \).