Cho \limits_{ - 3}^0 f( x )dx} = - 4\) và limits_{ - 3}^0 g( x )dx} = - 3\).

14/22

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

a) \(\int\limits_0^{ - 3} {f\left( x \right)dx} = - 4\).

b)\(\int\limits_{ - 3}^0 { - 3f\left( x \right)dx} = 12\).

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

d)\(\int\limits_{ - 3}^0 {\left[ {f\left( x \right) + 3x} \right]dx} = - 10\).

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Giải thích

a) S, b) Đ, c) Đ, d) S

a) \(\int\limits_0^{ - 3} {f\left( x \right)dx} = - \int\limits_{ - 3}^0 {f\left( x \right)dx} = 4\).

b) \(\int\limits_{ - 3}^0 { - 3f\left( x \right)dx} = - 3\int\limits_{ - 3}^0 {f\left( x \right)dx} = 12\).

c) \(\int\limits_{ - 3}^0 {\left[ {f\left( x \right) + g\left( x \right)} \right]dx} = \int\limits_{ - 3}^0 {f\left( x \right)dx} + \int\limits_{ - 3}^0 {g\left( x \right)dx} = - 4 + \left( { - 3} \right) = - 7\).

d) \(\int\limits_{ - 3}^0 {\left[ {f\left( x \right) + 3x} \right]dx} = \int\limits_{ - 3}^0 {f\left( x \right)dx} + \int\limits_{ - 3}^0 {3xdx} \)\( = - 4 + \left. {\frac{3}{2}{x^2}} \right|_{ - 3}^0\)\( = - 4 - \frac{{27}}{2} = - \frac{{35}}{2}\).