Bài 11. Cho biết \(\int\limits_1^2 {f\left( x \right)dx = - 4,} \) \(\int\limits_1^5 {f\left( x \right)dx = 6,} \) \(\int\limits_1^5 {g\left( x \right)} dx = 8.\) hãy tính
a) \(\int\limits_2^5 {f\left( x \right)} = \int\limits_2^1 {f\left( x \right)} dx + \int\limits_1^5 {f\left( x \right)} = - \int\limits_1^2 {f\left( x \right)} dx + \int\limits_1^5 {f\left( x \right)} dx = 4 + 6 = 10\)
b) \(\int\limits_1^2 {3f\left( x \right)} dx = 3\int\limits_1^2 {f\left( x \right)dx} = 3\left( { - 4} \right) = - 12\)
c) \(\int\limits_1^5 {\left[ {f\left( x \right) - g\left( x \right)} \right]} dx = \int\limits_1^5 {f\left( x \right)dx} - \int\limits_1^5 {g\left( x \right)} dx = 6 - 8 = - 2\)
d) \(\int\limits_1^5 {\left[ {4f\left( x \right) - g\left( x \right)} \right]} dx = 4\int\limits_1^5 {f\left( x \right)dx} - \int\limits_1^5 {g\left( x \right)dx = 4.6 - 8 = 16.} \)