JEE Main 202125 Jul, Morning shiftMathematicsMediumIntegral Calculus369× since 2002Let f:[0,∞)→[0,∞)f:[0,\infty ) \to [0,\infty )f:[0,∞)→[0,∞) be defined as f(x)=∫0x[y]dyf(x) = \int_0^x {[y]dy}f(x)=∫0x[y]dy where [x] is the greatest integer less than or equal to x. Which of the following is true?AOption A. f is continuous at every point in [0,∞)[0,\infty )[0,∞) and differentiable except at the integer points.BOption B. f is both continuous and differentiable except at the integer points in [0,∞)[0,\infty )[0,∞).COption C. f is continuous everywhere except at the integer points in [0,∞)[0,\infty )[0,∞).DOption D. f is differentiable at every point in [0,∞)[0,\infty )[0,∞).CheckSkip · show solution
