GATE 2018 EE – Question 28
Let $f$ be a real-valued function of a real variable defined as $f(x)=x-[x]$, where $[x]$ denotes the largest integer less than or equal to $x$. The value of $\displaystyle\int_{0.25}^{1.25}f(x)\,dx$ is ________ (up to 2 decimal places).
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Correct answer: 0.49 to 0.51
Explanation
On $[0.25,1)$, $f(x)=x$, giving $\frac{1-0.0625}{2}=0.46875$. On $[1,1.25]$, $f(x)=x-1$, giving $\frac{0.25^2}{2}=0.03125$. The total is $0.5$.