Q107 / 170 · Manipal (MET) 2018 · Mathematics

If $\int_{-1}^4 f(x) d x=4$ and $\int_2^4[3-f(x)] d x=7$, then the value of $\int_{-1}^2 f(x) d x$ is

  • A
    -2
  • B
    3
  • Correct answer
    C
    5
  • D
    8

Solution

$\int_2^4[3-f(x)] d x=7$ $\begin{array}{rr}\Rightarrow & {[3 x]_2^4-\int_2^4 f(x) d x=7} \\ \Rightarrow & 6-\int_2^4 f(x) d x=7 \\ \Rightarrow & \int_2^4 f(x) d x=-1...(i)\end{array}$ and $\int_{-1}^4 f(x) d x=4$ $\int_{-1}^4 f(x) d x=\int_{-1}^2 f(x) d x+\int_2^4 f(x) d x$ $\Rightarrow \quad 4=\int_{-1}^2 f(x) d x-1$ $\Rightarrow \quad \int_{-1}^2 f(x) d x=5$

Hence, the correct answer is option: 'C'.

Relevant Questions