Download App

STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
MCQ
Let $[x]$ denote the largest integer not exceeding $x$ and $\{x\}=x-[x]$. Then, $\int \limits_0^{2012} \frac{e^{\cos (\pi\{x\})}}{e^{\cos (\pi\{x\})}+e^{-\cos (\pi\{x\})}} d x$ is equal to
  • A
    $0$
  • ✓
    $1006$
  • C
    $2012$
  • D
    $2012\,\pi$
✓

Answer

Correct option: B.
$1006$
b
(b)

Explanation :-

$I =2012 \int \limits_0^1 \frac{e^{\cos \pi x}}{e^{\cos \pi x}+e^{-\cos \pi x}} d x$

using king property

$I =2012 \int \limits_0^1 \frac{e^{-\cos \pi x}}{e^{-\cos \pi x}+e^{\cos \pi x}} d x$

$\Rightarrow 2 I =2012 \Rightarrow I =1006$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The first term of an $A.P.$ of consecutive integers is ${p^2} + 1$ The sum of $(2p + 1)$ terms of this series can be expressed as
→
If the following system of linear equations

$2 x+y+z=5$

$x-y+z=3$

$x+y+a z=b$

has no solution, then :

→
Let $f(x) = {(x + 1)^2} - 1,\;\;(x \ge - 1)$. Then the set $S = \{ x:f(x) = {f^{ - 1}}(x)\} $ is
→
$\int_{}^{} {\frac{{{e^x}\;dx}}{{\sqrt {1 - {e^{2x}}} }} = } $
→
If $r = {[2\phi + {\cos ^2}(2\phi + \pi /4)]^{1/2}}$ then what is the value of the derivative of $dr/d\phi  $ at $\phi = \pi /4$
→
The term independent of $' x '$ in the expansion of ${\left( {9\,x, - frac{1}{{3\,\sqrt x }}} \right)^{18}}, x > 0$ , is $\alpha$ times the corresponding binomial co$-$efficient . Then $' \alpha \ '$ is :
→
If $a = i - j$ and $b = i + k$, then a unit vector coplanar with $a $ and  $ b $ and perpendicular to $a$  is
→
Let the expression $E = 8^a + 8^b -3.2^{a+b}$ takes its minimum value $'p'$ at $a = \alpha$ & $b = \beta $, then perpendicular distance of the point $P(\alpha , \beta )$ from the line $x + y + 2p = 0$ is
→
If ${a_1} = {a_2} = 2,\;{a_n} = {a_{n - 1}} - 1\;(n > 2)$, then ${a_5}$ is
→
If $2^{nd}$ order determinant with elements $0$ or $1$ is choosen isfrom set of all determinants, then find the probability that the determinant choosen is non - Zero
→