New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2021 · 16 Mar · Shift 2 · Q30

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

PYQ Library
JEE Main
Mathematics
Definite Integration
2021 · 16 Mar · Shift 2 · Q30

Definite Integration question

2021 · 16 Mar · Shift 2 · Q30

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1

Consider the integral

I = \int_0^{10} {{{[x]{e^{[x]}}} \over {{e^{x - 1}}}}dx}

, where [x] denotes the greatest integer less than or equal to x. Then the value of I is equal to :

A
45 (e $-$ 1)
B
45 (e + 1)
C
9 (e + 1)
D
9 (e $-$ 1)

More from Definite Integration

Let P(x) = x2 + bx + c be a quadratic polynomial with real coefficients such that $\int_{0}^{1} P (x) d x$ = 1 and P(x) leaves remainder 5 when it is divided by (x $-$ 2). Then the value of 9(b + c) is equal to :2021 · MCQ
Which of the following statements is correct for the function g( $α$ ) for $α \in$ R such that $g (α) = \frac{π}{6} \int \frac{π}{3} \frac{s i n ^{α} x}{c o s ^{α} x + s i n ^{α} x} d x$ 2021 · MCQ
If [ . ] represents the greatest integer function, then the value of $0 \int \frac{π}{2} [[x^{2}] - cos x] d x$ is .2021 · Numerical
Let f : R $\to$ R be defined as f(x) = e $-$ xsinx. If F : [0, 1] $\to$ R is a differentiable function with that F(x) = $\int_{0}^{x} f (t) d t$ , then the value of $\int_{0}^{1} (F^{'} (x) + f (x)) e^{x} d x$ lies in the interval2021 · MCQ
If the integral $\int_{0}^{10} \frac{[ s i n 2 π x ]}{e ^{x - [x]}} d x = α e^{- 1} + β e^{- \frac{1}{2}} + γ$ , where $α$ , $β$ , $γ$ are integers and [x] denotes the greatest integer less than or equal…2021 · MCQ
Let $I_{n} = \int_{1}^{e} x^{19} (lo g ∣ x ∣)^{n} d x$ , where n $\in$ N. If (20)I10 = $α$ I9 + $β$ I8, for natural numbers $α$ and $β$ , then $α - β$ equals to .2021 · Numerical
Let f(x) and g(x) be two functions satisfying f(x2) + g(4 $-$ x) = 4x3 and g(4 $-$ x) + g(x) = 0, then the value of $- 4 \int 4 f (x)^{2} d x$ is2021 · Numerical
Let g(x) = $\int_{0}^{x} f (t) d t$ , where f is continuous function in [ 0, 3 ] such that $\frac{1}{3} \leq$ f(t) $\leq$ 1 for all t $\in$ [0, 1] and 0 $\leq$ f(t) $\leq \frac{1}{2}$ for all t $\in$ (1, 3]. The largest possible interval in which…2021 · MCQ