(B) We need to evaluate $I = \int_{-1}^{2} \left[ \frac{[x]}{1 + x^2} \right] dx$. We split the integral based on the intervals of $[x]$: For $-1 \le

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(B) We need to evaluate $I = \int_{-1}^{2} \left[ \frac{[x]}{1 + x^2} \right] dx$. We split the integral based on the intervals of $[x]$: For $-1 \le x For $0 \le x For $1 \le x Therefore,$I = \int_{-1}^{0} (-1) dx + \int_{0}^{1} 0 dx + \int_{1}^{2} 0 dx = [-x]_{-1}^{0} + 0 + 0 = (0 - 1) = -1$.

Class 12 Mathematics 7-2.Definite Integral Fundamental definite integration

Evaluate the definite integral $\int_{-1}^{2} \left[ \frac{[x]}{1 + x^2} \right] dx$,where $[\cdot]$ denotes the Greatest Integer Function $(GIF)$.

A
$-2$
B
$-1$
C
$0$
D
None of these

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7-2.Definite Integral

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Fundamental definite integration

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Evaluate the definite integral $\int_{-1}^{2} \left[ \frac{[x]}{1 + x^2} \right] dx$,where $[\cdot]$ denotes the Greatest Integer Function $(GIF)$.

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