Question

\(\int_{0}^{2}\left[x^{2}\right] d x\) is equal to
(A) 1
(B) \(5-\sqrt{2}-\sqrt{3}\)
(C) \(3-\sqrt{2}\)
(D) \(8 / 3\)

Answer 1

Ans : (B)
Hint : \(\int_{0}^{1} 0 d x+\int_{1}^{\sqrt{2}} 1 \cdot d x+\int_{\sqrt{2}}^{\sqrt{3}} 2 \cdot d x+\int_{\sqrt{3}}^{2} 3 d x\)
$$
=5-\sqrt{2}-\sqrt{3}
$$