New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Definite Integration question

2017 · Shift 2 · Q27

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

PYQ Library
JEE Advanced
Mathematics
Definite Integration
2017 · Shift 2 · Q27

Definite Integration question

2017 · Shift 2 · Q27

JEE AdvancedMathematicsDefinite IntegrationMultiple correct+4 / −2

If

I = \sum olimits_{k = 1}^{98} {\int_k^{k + 1} {{{k + 1} \over {x(x + 1)}}} dx}

, then

A
$I \gt {\log _e}99$
B
$I \lt {\log _e}99$
C
$I \lt {{49} \over {50}}$
D
$I \gt {{49} \over {50}}$

More from Definite Integration

The total number of distinct $x \in [0, 1]$ for which $0 \int x \frac{t ^{2}}{1 + t ^{4}} d t = 2 x - 1$ 2016 · Numerical
Let $f (x) = n \to \infty lim (\frac{n ^{n} ( x + n ) ( x + \frac{n}{2} ) ... ( x + \frac{n}{n} )}{n ! ( x ^{2} + n ^{2} ) ( x ^{2} + \frac{n ^{2}}{4} ) .... ( x ^{2} + \frac{n ^{2}}{n ^{2}} )})^{\frac{x}{n}},$ …2016 · Multiple correct
The value of $- \frac{π}{2} \int \frac{π}{2} \frac{x ^{2} c o s x}{1 + e ^{x}} d x$ is equal to2016 · MCQ
Let $f : R \to R$ be a function defined by $f (x) = {[x], 0, x \leq 2 x > 2$ where $[x]$ is the greatest integer less than or…2015 · Numerical
Let $f (x) = 7 tan^{8} x + 7 tan^{6} x - 3 tan^{4} x - 3 tan^{2} x$ for all $x \in (- \frac{π}{2}, \frac{π}{2}) .$ Then the correct expression(s) is (are)2015 · Multiple correct
The option(s) with the values of a and $L$ that satisfy the following equation is (are) $\frac{0 \int 4 π e ^{t} ( s i n ^{6} a t + c o s ^{4} a t ) d t}{0 \int π e ^{t} ( s i n ^{6} a t + c o s ^{4} a t ) d t} = L ?$ …2015 · Multiple correct
Let $f^{'} (x) = \frac{192 x ^{3}}{2 + s i n ^{4} π x}$ for all $x \in R$ with $f (\frac{1}{2}) = 0$ . If $m \leq 1/2 \int 1 f (x) d x \leq M,$ then the possible values of $m$ and…2015 · MCQ
If $α = 0 \int 1 (e^{9 x + 3 t a n^{- 1} x}) (\frac{12 + 9 x ^{2}}{1 + x ^{2}}) d x$ where $tan^{- 1} x$ takes only principal values, then the value of $(lo g_{e} ∣ 1 + α ∣ - \frac{3 π}{4})$ …2015 · Numerical