Question

If \([t]\) denotes the greatest integer function, then \[ \int_{-2}^{2} \left[ \frac{x^2+[x+1]} {1+x^2} \right]dx = \ ? \]

• A. \(2\tan^{-1}2\)
• B. \(0\)
• C. \(\sqrt2\)
• D. \(\tan^{-1}2\)

Hint:

For greatest integer function integrals, always split the interval at integer points where the GIF changes value.

Answer 1

The Correct Option is B