Cho tích phân - 2^2 f( x )dx = 1, tích phân - 2^4 f( t )dt = - 4. Tính tích phân 2^4 f( y )dy

10/25

Cho \(\int\limits_{ - 2}^2 {f\left( x \right){\rm{d}}x} = 1\), \(\int\limits_{ - 2}^4 {f\left( t \right){\rm{d}}t} = - 4\). Tính \(\int\limits_2^4 {f\left( y \right){\rm{d}}y} \).

\(I = 5\).

\(I = - 3\).

\(I = 3\).

\(I = - 5\).

Giải thích

chọn D

Ta có: \(\int\limits_{ - 2}^4 {f\left( t \right){\rm{d}}t} = \int\limits_{ - 2}^4 {f\left( x \right){\rm{d}}x} \), \(\int\limits_2^4 {f\left( y \right){\rm{d}}y} = \int\limits_2^4 {f\left( x \right){\rm{d}}x} \).

Khi đó: \[\int\limits_{ - 2}^2 {f\left( x \right){\rm{d}}x} + \int\limits_2^4 {f\left( x \right){\rm{d}}x} = \int\limits_{ - 2}^4 {f\left( x \right){\rm{d}}x} \].

\( \Rightarrow \int\limits_2^4 {f\left( x \right){\rm{d}}x} = \int\limits_{ - 2}^4 {f\left( x \right){\rm{d}}x} - \int\limits_{ - 2}^2 {f\left( x \right){\rm{d}}x} = - 4 - 1 = - 5\).

Vậy \(\int\limits_2^4 {f\left( y \right){\rm{d}}y} = - 5\).