Giải bài tập 4.9 trang 18

Đề bài

Cho $\underset{0}{\overset{3}{\int }}f\left(x\right)dx=5$ và $\underset{0}{\overset{3}{\int }}g\left(x\right)dx=2$. Tính:

a) $\underset{0}{\overset{3}{\int }}\left[f\left(x\right)+g\left(x\right)\right]dx$;

b) $\underset{0}{\overset{3}{\int }}\left[f\left(x\right)-g\left(x\right)\right]dx$;

c) $\underset{0}{\overset{3}{\int }}3f\left(x\right)dx$;

d) $\underset{0}{\overset{3}{\int }}\left[2f\left(x\right)-3g\left(x\right)\right]dx$.

Lời giải chi tiết

a) $\underset{0}{\overset{3}{\int }}\left[f\left(x\right)+g\left(x\right)\right]dx$

$=\underset{0}{\overset{3}{\int }}f\left(x\right)dx+\underset{0}{\overset{3}{\int }}g\left(x\right)dx$

$=5+2=7$.

b) $\underset{0}{\overset{3}{\int }}\left[f\left(x\right)-g\left(x\right)\right]dx$

$=\underset{0}{\overset{3}{\int }}f\left(x\right)dx-\underset{0}{\overset{3}{\int }}g\left(x\right)dx$

$=5-2=3$.

c) $\underset{0}{\overset{3}{\int }}3f\left(x\right)dx=3\underset{0}{\overset{3}{\int }}f\left(x\right)dx$

$=3.5=15$.

d) $\underset{0}{\overset{3}{\int }}\left[2f\left(x\right)-3g\left(x\right)\right]dx$

$=2\underset{0}{\overset{3}{\int }}f\left(x\right)dx-3\underset{0}{\overset{3}{\int }}g\left(x\right)dx$

$=2.5-3.2=4$.