Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^2\left[x^2\right] d x=$
A
$5+\sqrt{2}-\sqrt{3}$
B
$-5-\sqrt{2}-\sqrt{3}$
✓
$5-\sqrt{2}-\sqrt{3}$
D
$5-\sqrt{2}+\sqrt{3}$
✓
Answer
Correct option: C.
$5-\sqrt{2}-\sqrt{3}$
(C) $\int_0^2\left[x^2\right] d x$ $\begin{array}{l}=\int_0^1\left[x^2\right] d x+\int_1^{\sqrt{2}}\left[x^2\right] d x+\int_{\sqrt{2}}^{\sqrt{3}}\left[x^2\right] d x+\int_{\sqrt{3}}^2\left[x^2\right] d x \\ =\int_0^1 0 d x+\int_1^{\sqrt{2}} 1 d x+\int_{\sqrt{2}}^{\sqrt{3}} 2+\int_{\sqrt{3}}^2 3 d x \\ =0+[x]_1^{\sqrt{2}}+2[x]_{\sqrt{2}}^{\sqrt{3}}+3[x]_{\sqrt{3}}^2 \\ =(\sqrt{2}-1)+2(\sqrt{3}-\sqrt{2})+3(2-\sqrt{3}) \\ =5-\sqrt{2}-\sqrt{3}\end{array}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.