Question

If $\underset{-1}{\overset{4}{\int }}f\left(x\right)dx=4$ and $\underset{2}{\overset{4}{\int }}\left\{3-f\left(x\right)\right\}dx=7$, then the value of $\underset{-1}{\overset{2}{\int }}f\left(x\right)dx$ is

• A. $-2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (D)

Since, $\underset{2}{\overset{4}{\int }}\left\{3-f\left(x\right)\right\}dx=7$

$\Rightarrow 3{\left[x\right]}_2^4-\underset{2}{\overset{4}{\int }}f\left(x\right)dx=7$

$\Rightarrow \underset{2}{\overset{4}{\int }}f\left(x\right)dx=6-7=-1$

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

$=4-\left(-1\right)=5$