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) \(\int\limits_1^9 { - 2f\left( x \right)} dx;\) \(b)\,\int\limits_7^9 {\left[ {f\left( x \right) + g\left( x \right)} \right]} dx;\)
\(c)\,\int\limits_7^9 {\left[ {2f\left( x \right) - 3g\left( x \right)} \right]dx;} \) \(d)\,\int\limits_1^7 {f\left( x \right)} dx;\)
Advertisements (Quảng cáo)
a) \(\int\limits_1^9 { - 2f\left( x \right)} dx = - 2\int\limits_1^9 {f\left( x \right)dx = - 2\left( { - 1} \right)} = 2\)
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) \(\int\limits_1^7 {f\left( x \right)} dx = \int\limits_1^9 {f\left( x \right)} dx + \int\limits_9^7 {f\left( x \right)} dx = \int\limits_1^9 {f\left( x \right)} dx - \int\limits_7^9 {f\left( x \right)} dx = - 1 - 5 = - 6\)