Q86 / 200 · TS EAMCET 2001 · Mathematics

Evaluate $\int_{-2}^1 f(x) d x$, where $f(x)= \begin{cases}1-2 x, & x \leq 0 \\ 1+2 x, & x \geq 0\end{cases}$

  • A
    $0$
  • B
    $2$
  • Correct answer
    C
    $4$
  • D
    $6$

Solution

$\begin{array}{rl}\int_{-1}^1 f(x) d x=\int_{-1}^0 & f(x) d x+\int_0^1 f(x) d x \\ & =\int_{-1}^0(1-2 x) d x+\int_0^1(1+2 x) d x \\ & =\left[x-x^2\right]_{-1}^0+\left[x+x^2\right]_0^1\end{array}$ $=-(-1-1)+[1+1]=2+2=4$

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

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