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Bài 46. Cho biết \(\int\limits_1^9 {f\left( x \right)dx} = – 1,\int\limits_7^9 {f\left( x \right)} dx = 5,\int\limits_7^9 {g\left( x \right)} dx = 4.\)
Hãy tìm:
a) \(\int\limits_1^9 { – 2f\left( x \right)} dx;\) \(b)\,\int\limits_7^9 {\left[ {f\left( x \right) + g\left( x \right)} \right]} dx;\)
\(c)\,\int\limits_7^9 {\left[ {2f\left( x \right) – 3g\left( x \right)} \right]dx;} \) \(d)\,\int\limits_1^7 {f\left( x \right)} dx;\)
a) \(\int\limits_1^9 { – 2f\left( x \right)} dx = – 2\int\limits_1^9 {f\left( x \right)dx = – 2\left( { – 1} \right)} = 2\)
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b) \(\int\limits_7^9 {\left[ {f\left( x \right) + g\left( x \right)} \right]} dx = \int\limits_7^9 {f\left( x \right)} dx + \int\limits_7^9 {g\left( x \right)} dx = 5 + 4 = 9\)
c) \(\int\limits_7^9 {\left[ {2f\left( x \right) – 3g\left( x \right)} \right]dx = } 2\int\limits_7^9 {f\left( x \right)} dx – 3\int\limits_7^9 {g\left( x \right)} dx = 2.5 – 3.4 = – 2\)
d) \(\int\limits_1^7 {f\left( x \right)} dx = \int\limits_1^9 {f\left( x \right)} dx + \int\limits_9^7 {f\left( x \right)} dx = \int\limits_1^9 {f\left( x \right)} dx – \int\limits_7^9 {f\left( x \right)} dx = – 1 – 5 = – 6\)