Cho \(\int\limits_{ - 3}^0 {f\left( x \right){\rm{d}}x} = - 4\) và \(\int\limits_{ - 3}^0 {g\left( x \right){\rm{d}}x} = - 3\).

7/50

a) \(\int\limits_{ - 3}^0 {\left[ {f\left( x \right) + g\left( x \right)} \right]{\rm{d}}x} = - 7\).

b) \[\int\limits_{ - 3}^0 {\left[ {f\left( x \right) - g\left( x \right)} \right]{\rm{d}}x} = 1\].

c) \(\int\limits_{ - 3}^0 {\left[ { - 3f\left( x \right)} \right]{\rm{d}}x} = 12\).

d)\[\int\limits_{ - 3}^0 {\left[ {2f\left( x \right) + 3g\left( x \right)} \right]{\rm{d}}x} = - 51\].

Nhập câu trả lời ở đây

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Giải thích

Ta có: \(\int\limits_{ - 3}^0 {\left[ {f\left( x \right) + g\left( x \right)} \right]{\rm{d}}x} = \int\limits_{ - 3}^0 {f\left( x \right){\rm{d}}x} + \int\limits_{ - 3}^0 {g\left( x \right){\rm{d}}x} = \left( { - 4} \right) + \left( { - 3} \right) = - 7\).

\[\int\limits_{ - 3}^0 {\left[ {f\left( x \right) - g\left( x \right)} \right]{\rm{d}}x} \]\( = \int\limits_{ - 3}^0 {f\left( x \right){\rm{d}}x} - \int\limits_{ - 3}^0 {g\left( x \right){\rm{d}}x} = \left( { - 4} \right) - \left( { - 3} \right) = - 1\).

\(\int\limits_{ - 3}^0 {\left[ { - 3f\left( x \right)} \right]{\rm{d}}x} = \left( { - 3} \right) \cdot \int\limits_{ - 3}^0 {f\left( x \right){\rm{d}}x} = \left( { - 3} \right) \cdot \left( { - 4} \right) = 12\).

\[\int\limits_{ - 3}^0 {\left[ {2f\left( x \right) + 3g\left( x \right)} \right]{\rm{d}}x} = 2\int\limits_{ - 3}^0 {f\left( x \right){\rm{d}}x} + 3\int\limits_{ - 3}^0 {g\left( x \right){\rm{d}}x} \]\( = 2 \cdot \left( { - 4} \right) + 3 \cdot \left( { - 3} \right) = - 17\).

Đáp án: a) Đúng, b) Sai, c) Đúng, d) Sai.