Cho I = 3 landa -1 | 2x -4 || dx

3/22

Cho \(I = \int\limits_{ - 1}^3 {\left| {2x - 4} \right|{\rm{d}}x} \). Chọn khẳng định đúng.

\(I = \left| {\int\limits_{ - 1}^3 {\left( {2x - 4} \right){\rm{d}}x} } \right|\).

\(I = - \int\limits_{ - 1}^2 {\left( {2x - 4} \right){\rm{d}}x + } \int\limits_2^3 {\left( {2x - 4} \right){\rm{d}}x} \).

\(I = \int\limits_{ - 1}^2 {\left( {2x - 4} \right){\rm{d}}x + } \int\limits_2^3 {\left( {2x - 4} \right){\rm{d}}x} \).

\(I = \int\limits_{ - 1}^2 {\left( {2x - 4} \right){\rm{d}}x - } \int\limits_2^3 {\left( {2x - 4} \right){\rm{d}}x} \).

Giải thích

Ta thấy \(2x - 4 \ge 0 \Leftrightarrow x \ge 2\).

Vậy \(I = \int\limits_{ - 1}^3 {\left| {2x - 4} \right|{\rm{d}}x} \)\( = - \int\limits_{ - 1}^2 {\left( {2x - 4} \right){\rm{d}}x + } \int\limits_2^3 {\left( {2x - 4} \right){\rm{d}}x} \).