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7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
Let $[ x ]$ denote the greatest integer $\leq x$. Consider the function $f(x)=\max \left\{x^2, 1+[x]\right\}$. Then the value of the integral $\int \limits_0^2 f ( x ) dx$ is :
  • ✓
    $\frac{5+4 \sqrt{2}}{3}$
  • B
    $\frac{8+4 \sqrt{2}}{3}$
  • C
    $\frac{1+5 \sqrt{2}}{3}$
  • D
    $\frac{4+5 \sqrt{2}}{3}$
✓

Answer

Correct option: A.
$\frac{5+4 \sqrt{2}}{3}$
a
$A=\int \limits_0^1 1 . d x+\int \limits_1^{\sqrt{2}} 2 d x+\int \limits_{\sqrt{2}}^2 x^2 d x$

$=1+2 \sqrt{2}-2+\frac{8}{3}-\frac{2 \sqrt{2}}{3}$

$=\frac{5}{3}+\frac{4 \sqrt{2}}{3}$

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