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The value of the integral, \( \int_{1}^{3}\left[x^{2}-2 x-2\right] d x \), where \( [x] \) denotes the greatest integer …

Q1

The value of the integral, \( \int_{1}^{3}\left[x^{2}-2 x-2\right] d x \), where \( [x] \) denotes the greatest integer less than or equal to \( x \) is:

[JEE Main 2021, 24 Feb (Shift 2)]

a

\( -5 \)

b

\( -\sqrt{2}-\sqrt{3}+1 \)

c

\( -4 \)

d

\( -\sqrt{2}-\sqrt{3}-1 \)

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