Cho F ( x ) là một nguyên hàm của f ( x ) = 2/x . Biết F ( − 1 ) = 0 . Tính F ( 2 ) kết quả là.

10/25

Cho \(F\left( x \right)\) là một nguyên hàm của \(f\left( x \right) = \frac{2}{x}\). Biết \(F\left( { - 1} \right) = 0\). Tính \(F\left( 2 \right)\) kết quả là.

\(2\ln 2 + 1\).

\(\ln 2\).

\(2\ln 3 + 2\).

\(2\ln 2\).

Giải thích

Đáp án đúng là: D

Ta có: \(\int\limits_{ - 1}^2 {f(x)dx = \left. {F\left( x \right)} \right|_{ - 1}^2 = F\left( 2 \right) - F\left( { - 1} \right)} \).

\[\int\limits_{ - 1}^2 {f(x)dx = } \int\limits_{ - 1}^2 {\frac{2}{x}} = \left. {2\ln \left| x \right|} \right|_{ - 1}^2 = 2\ln 2 - 2\ln 1 = 2\ln 2\].

\( \Rightarrow F\left( 2 \right) - F\left( { - 1} \right) = 2\ln 2\)

\( \Leftrightarrow F\left( 2 \right) = 2\ln 2\) (do \(F\left( { - 1} \right) = 0\)).