Download App

Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
If $I =\int_{1 / e}^{ e }|\log x| \frac{ d x}{x^2}$, then I is equal to
  • A
    2
  • B
    $\frac{2}{ e }$
  • ✓
    $2\left(1-\frac{1}{ e }\right)$
  • D
    $0$
✓

Answer

Correct option: C.
$2\left(1-\frac{1}{ e }\right)$
(C)
Since $|\log x|=-\log x$, if $\frac{1}{ e }<x<1$
$=\log x$, if $1<x< e$
$\therefore I =\int_{1 / e }^1 \frac{(-\log x)}{x^2} d x+\int_1^{ e } \frac{\log x}{x^2} d x$
$=-\left[-\frac{\log x}{x}-\frac{1}{x}\right]_{1 / e }^1+\left[-\frac{\log x}{x}-\frac{1}{x}\right]_1^{ e } \\ =\left[0+1-\left(\frac{\log \frac{1}{ e }}{\frac{1}{ e }}+\frac{1}{\frac{1}{ e }}\right)\right]-\left[\frac{\log e }{ e }+\frac{1}{ e }-(0+1)\right] \\ =1-(- e + e )-\left(\frac{2}{ e }-1\right) \\ =2-\frac{2}{ e }=2\left(1-\frac{1}{ e }\right)$

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

More "MCQ" from Definite Integration→Definite Integration — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If a line makes angles $45^{\circ}, 60^{\circ}$ and $60^{\circ}$ with the $X , Y$ and Z -axes respectively, then its direction cosines are
→
If the vector equation of a plane passing through three points $\left(1,0, z_1\right),(1,-1,1)$, and $(4,-3,2)$ is $\bar{r} \cdot(-\hat{i}+3 \hat{k})=2$, then the value of $z_1$ is
→
The co-ordinates of a point P are $(3,12,4)$ with respect to origin O , then the direction cosines of OP are
→
$\sin ^{-1} x+\cos ^{-1} x$ is equal to
→
$\int_0^{\pi / 2} \frac{\sin x \cos x}{1+\sin ^4 x} d x=$
→
If $\int_0^k \frac{1}{2+8 x^2} d x=\frac{\pi}{16}$, then the value of $k$ is.....
→
$6 x^2+h x y+12 y^2=0$ represents pair of parallel straight lines, if $h$ is
→
If $U =\left[\begin{array}{ll}\frac{1}{\sqrt{2}} & \frac{-1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{2}}\end{array}\right]$, then $U ^{-1}$ is
→
If $x=f(t)$ and $y=g(t)$ are difterentiable functions of t, then $\frac{d^2 y}{d x^2}$ is
→
$2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{5 \sqrt{2}}{7}+2 \tan ^{-1} \frac{1}{8}=$
→