Mathematics · 2021
JEE Main · 25 July 2021, Shift 1 · Q64
Let f:[0, ∞) →[0, ∞) be defined as f(x)=∫_0^x[y] d y where [x] is the greatest integer less than or equal to x. Which of the following is true?
Let $\displaystyle f:[0, \infty) \rightarrow[0, \infty)$ be defined as
$$f(x)=\int_0^x[y] \mathrm{d} y
$$
where $\displaystyle [x]$ is the greatest integer less than or equal to $\displaystyle x$. Which of the following is true ?
Official answer
(2)
$\displaystyle f$ is continuous at every point in $\displaystyle [0, \infty)$ and differentiable except at the integer points.
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JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.