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The area of the region bounded by y=x–[x] and 2x–1=0 and X–axis is

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$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{8}$

answer is C.

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Detailed Solution

$y = x - [x] and x = \frac{1}{2} intersect at (\frac{1}{2}, \frac{1}{2})$

Area= $\frac{1}{2} (\frac{1}{2} \times \frac{1}{2}) = \frac{1}{8}$

$\int_{0}^{\frac{1}{2}} (x - [x]) d x = \int_{0}^{\frac{1}{2}} (x) d x = {(\frac{x^{2}}{2})}_{0}^{1 / 2} = \frac{1}{8}$

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