Q114 / 160 · TS EAMCET 2023 (14 May Shift 1) · Mathematics

$\int_{-1}^1 x|x| d x=$

  • A
    $1$
  • B
    $\frac{1}{2}$
  • Correct answer
    C
    $0$
  • D
    $\frac{2}{3}$

Solution

$\int_{-1}^1 x|x| d x$ $\begin{aligned} & =\int_{-1}^0 x(-x) d x+\int_0^1 x \cdot x d x \\ & =-\int_{-1}^0 x^2 d x+\int_0^1 x^2 d x \\ & =-\left[\frac{x^3}{3}\right]_{-1}^0+\left[\frac{x^3}{3}\right]_0^1 \\ & =-\left(0+\frac{1}{3}\right)+\left(\frac{1}{3}-0\right)=0\end{aligned}$

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

Relevant Questions