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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate: $\int_0^2(x-[x]) d x$
  • A
    0
  • B
    -1
  • C
    1
  • D
    2
✓

Answer

$
\begin{array}{l}
\text { (c) : Let } I=\int_0^2(x-[x]) d x=\int_0^2 x d x-\int_0^2[x] d x \\
=\left[\frac{x^2}{2}\right]_0^2-\int_0^1[x] d x-\int_1^2[x] d x=\frac{4}{2}-\int_0^1 0 d x-\int_1^2 1 d x \\
=2-0-[x]_1^2=2-[2-1]=2-1=1
\end{array}
$

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