Giải bài 40 trang 22

Đề bài

Cho $\underset{-2}{\overset{1}{\int }}f\left(x\right)dx=5$ và $\underset{-2}{\overset{1}{\int }}g\left(x\right)dx=-4$. Tính:

a) $\underset{1}{\overset{-2}{\int }}f\left(x\right)dx$;

b) $\underset{-2}{\overset{1}{\int }}-4f\left(x\right)dx$;

c) $\underset{-2}{\overset{1}{\int }}\frac{-2g\left(x\right)}{3}dx$;

d) $\underset{-2}{\overset{1}{\int }}\left[f\left(x\right)+g\left(x\right)\right]dx$;

e) $\underset{-2}{\overset{1}{\int }}\left[f\left(x\right)-g\left(x\right)\right]dx$;

g) $\underset{-2}{\overset{1}{\int }}\left[3f\left(x\right)-5g\left(x\right)\right]dx$.

Lời giải chi tiết

a) $\underset{1}{\overset{-2}{\int }}f\left(x\right)dx=-\underset{-2}{\overset{1}{\int }}f\left(x\right)dx=-5$.

b) $\underset{-2}{\overset{1}{\int }}-4f\left(x\right)dx=-4\underset{-2}{\overset{1}{\int }}f\left(x\right)dx=-4.5=-20$.

c) $\underset{-2}{\overset{1}{\int }}\frac{-2g\left(x\right)}{3}dx=\frac{-2}{3}\underset{-2}{\overset{1}{\int }}g\left(x\right)dx=\frac{-2}{3}.\left(-4\right)=\frac{8}{3}$.

d) $\underset{-2}{\overset{1}{\int }}\left[f\left(x\right)+g\left(x\right)\right]dx=\underset{-2}{\overset{1}{\int }}f\left(x\right)dx+\underset{-2}{\overset{1}{\int }}g\left(x\right)dx=5+\left(-4\right)=1$.

e) $\underset{-2}{\overset{1}{\int }}\left[f\left(x\right)-g\left(x\right)\right]dx=\underset{-2}{\overset{1}{\int }}f\left(x\right)dx-\underset{-2}{\overset{1}{\int }}g\left(x\right)dx=5-\left(-4\right)=9$.

g) $\underset{-2}{\overset{1}{\int }}\left[3f\left(x\right)-5g\left(x\right)\right]dx=3\underset{-2}{\overset{1}{\int }}f\left(x\right)dx-5\underset{-2}{\overset{1}{\int }}g\left(x\right)dx=3.5-5.\left(-4\right)=35$.