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Definite Integrals — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integrals2 Marks
Question
$\int\limits^{1}_0\{\text{x}\}\text{dx},$ where {x} denotes the fractional part of x.
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Answer

We have,$\text{I}=\int\limits^{1}_0\{\text{x}\}\text{dx}$
We know $\{\text{x}\}=\text{x},0<\text{x}<1$$\therefore\ \text{I}=\int\limits^{1}_0\{\text{x}\}\text{dx}$
$=\Big[\frac{\text{x}^2}{2}\Big]^1_0$
$=\frac{1}{2}-\frac{0}{2}$
$=\frac{1}{2}$

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