Q116 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics

$\int_{-1}^1\left(\sqrt{1+x+x^2}-\sqrt{1-x+x^2}\right) d x=$

  • A
    2
  • B
    4
  • Correct answer
    C
    0
  • D
    8

Solution

$\begin{aligned} & \text { } \int_{-a}^a f(x) d x=\int_0^a[f(x)+f(-x)] d x \\ & =\int_0^1\left(\sqrt{1+x+x^2}-\sqrt{1-x+x^2}\right) d x \\ & +\int_0^1\left(\sqrt{1-x+x^2}-\sqrt{1+x+x^2}\right) d x=\int_0^1 0 \cdot d x=0 .\end{aligned}$

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

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