Question

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

• A. $-2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (D)

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

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

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

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

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