Bài 46 Trang 176 SGK Đại số và Giải tích 12 Nâng cao

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) \(\int\limits_1^9 { - 2f\left( x \right)} dx =  - 2\int\limits_1^9 {f\left( x \right)dx =  - 2\left( { - 1} \right)}  = 2\)

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) \(\int\limits_1^7 {f\left( x \right)} dx = \int\limits_1^9 {f\left( x \right)} dx + \int\limits_9^7 {f\left( x \right)} dx = \int\limits_1^9 {f\left( x \right)} dx - \int\limits_7^9 {f\left( x \right)} dx =  - 1 - 5 =  - 6\)