Question

If ${\int }_{-1}^{4}f\left(x\right)dx=4$ and ${\int }_2^4\{3-f\left(x\right)\}dx=7$, then the value of ${\int }_{-1}^{2}f\left(x\right)dx$ is

• A. $-2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (D)

$5$

Since, ${\int }_2^4\{3-f\left(x\right)\}dx=7$
$\Rightarrow 3{\left[x\right]}_2^4-{\int }_2^{4}f\left(x\right)dx=7$
$\Rightarrow {\int }_2^{4}f\left(x\right)dx=6-7=-1$
$\therefore {\int }_{-1}^{2}f\left(x\right)dx={\int }_{-1}^{4}f\left(x\right)dx-{\int }_2^{4}f\left(x\right)dx$
$=4-(-1)=5$