New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2021 · 25 Jul · Shift 1 · Q33

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Definite Integration
2021 · 25 Jul · Shift 1 · Q33

Definite Integration question

2021 · 25 Jul · Shift 1 · Q33

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Let

f:[0,\infty ) \to [0,\infty )

be defined as

f(x) = \int_0^x {[y]dy}

where [x] is the greatest integer less than or equal to x. Which of the following is true?

A
f is continuous at every point in $[0,\infty )$ and differentiable except at the integer points.
B
f is both continuous and differentiable except at the integer points in $[0,\infty )$ .
C
f is continuous everywhere except at the integer points in $[0,\infty )$ .
D
f is differentiable at every point in $[0,\infty )$ .

More from Definite Integration

If $f (x) = ⎩ ⎨ ⎧ 0 \int x (5 + ∣ 1 - t ∣) d t, 5 x + 1, x > 2 x \leq 2$ , then2021 · MCQ
The value of the integral $- 1 \int 1 lo g (x + x^{2} + 1) d x$ is :2021 · MCQ
The value of $\frac{- 1}{2} \int \frac{1}{2} ((\frac{x + 1}{x - 1})^{2} + (\frac{x - 1}{x + 1})^{2} - 2)^{\frac{1}{2}} d x$ is :2021 · MCQ
If the value of the integral $0 \int 5 \frac{x + [ x ]}{e ^{x - [x]}} d x = α e^{- 1} + β$ , where $α$ , $β \in$ R, 5 $α$ + 6 $β$ = 0, and [x] denotes the greatest integer less than or equal to x;…2021 · MCQ
The value of $- \frac{π}{2} \int \frac{π}{2} (\frac{1 + s i n ^{2} x}{1 + π ^{s i n x}}) d x$ is2021 · MCQ
The value of $- π /2 \int π /2 \frac{c o s ^{2} x}{1 + 3 ^{x}} d x$ is :2021 · MCQ
The value of $n = 1 \sum 100 n - 1 \int n e^{x - [x]} d x$ , where [ x ] is the greatest integer $\leq$ x, is :2021 · MCQ
The value of the integral $0 \int π ∣ sin 2 x ∣ d x$ is .2021 · Numerical