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
$\int_0^1 {\frac{{\log x}}{{\sqrt {1 - {x^2}} }}\,dx = } $
  • A
    $\frac{\pi }{2}\log 2$
  • B
    $\pi \log 2$
  • ✓
    $ - \frac{\pi }{2}\log 2$
  • D
    $ - \pi \log 2$
✓

Answer

Correct option: C.
$ - \frac{\pi }{2}\log 2$
c
(c) Put $x = \sin \theta ,$ we get

$\int_0^1 {\frac{{\log x}}{{\sqrt {1 - {x^2}} }}dx }$

$={ \int_0^{\pi /2} {\frac{{\log \sin \theta .\cos \theta }}{{\cos \theta }}} } \,d\theta $

$ = \int_0^{\pi /2} {\,\log \sin \theta } \,d\theta = - \frac{\pi }{2}\log 2$.

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 roots of ${(2 - 2i)^{1/3}}$ are
→
If direction ratios of two lines are $5,\,\, - 12,\,13$ and $ - 3,\,4,\,5$ then the angle between them is
→
If $\tan \left(\frac{\pi}{9}\right), x, \tan \left(\frac{7 \pi}{18}\right)$ are in arithmetic progression and $\tan \left(\frac{\pi}{9}\right), y, \tan \left(\frac{5 \pi}{18}\right)$ are also in arithmetic progression, then $|x-2 y|$ is equal to:
→
$\mathop {\lim }\limits_{x \to 0} \frac{{{4^x} - {9^x}}}{{x({4^x} + {9^x})}} = $
→
Let the area of the region enclosed by the curves $y=3 x, 2 y=27-3 x$ and $y=3 x-x \sqrt{x}$ be $A$. Then $10 \mathrm{~A}$ is equal to
→
Suppose the parabola $(y-h)^2=4(x-h)$, with vertex $A$, passes through $O=(0,0)$ and $L=(0,2)$. Let $D$ be an end point of the latusrectum. Let the $Y$-axis intersect the axis of the parabola at $P$. Then, $\angle P D A$ is equal to
→
$\int_{}^{} {\sqrt {1 + {x^2}} \;dx = } $
→
There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by $66$ the number of games that the men played with the women. The number of participants is
→
The number of divisors of $9600$ including $1$ and $9600$ are
→
If the straight lines $\frac{x-1}{2}=\frac{y+1}{k}=\frac{z}{2}$ and $\frac{x+1}{5}=\frac{y+1}{2}=\frac{z}{k}$ are coplanar, then the plane$(s)$ containing these two lines is(are)

$(A)$ $y+2 z=-1$ $(B)$ $y+z=-1$ $(C)$ $y-z=-1$ $(D)$ $y-2 z=-1$

→