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
If $\int_0^k {\frac{{dx}}{{2 + 8{x^2}}}} = \frac{\pi }{{16}}\,,$ then $k = $
  • A
    $1$
  • ✓
    $\frac{1}{2}$
  • C
    $\frac{1}{4}$
  • D
    None of these
✓

Answer

Correct option: B.
$\frac{1}{2}$
b
(b) $\int_0^k {\frac{1}{{2 + 8{x^2}}}dx = \frac{1}{2}\int_0^k {\frac{{dx}}{{1 + {{(2x)}^2}}}= \frac{1}{4}\int_0^{2k} {\frac{{dt}}{{1 + {t^2}}}} } } $

$ = \frac{1}{4}|{\tan ^{ - 1}}t|_0^{2k} = \frac{1}{4}{\tan ^{ - 1}}2k$.

Comparing it with the given value, we get

${\tan ^{ - 1}}2k = \frac{\pi }{4} $

$\Rightarrow 2k = 1$

$ \Rightarrow k = \frac{1}{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 diagonals of a parallelogram $PQRS$ are along the lines $x + 3y = 4$ and $6x - 2y = 7$. Then $PQRS$ must be a
→
The value of $\mathop {\lim }\limits_{a \to 0} \frac{{\sin a - \tan a}}{{{{\sin }^3}a}}$ will be
→
Let $i=\sqrt{-1}$. If $\frac{(-1+i \sqrt{3})^{21}}{(1-i)^{24}}+\frac{(1+i \sqrt{3})^{21}}{(1+i)^{24}}=k$, and $n =[| k |]$ be the greatest integral part of $| k |$. Then $\sum_{ j =0}^{ n +5}( j +5)^{2}-\sum_{ j =0}^{ n +5}( j +5)$ is equal to ........ .
→
If  ${\log _{\tan {{30}^ \circ }}}\left( {\frac{{2{{\left| z \right|}^2} + 2\left| z \right| - 3}}{{\left| z \right| + 1}}} \right)\, < \, - 2$ then
→
Let $T$ be the tangent to the ellipse $E: x^{2}+4 y^{2}=5$ at the point $P(1,1)$. If the area of the region bounded by the tangent $T$, ellipse $E$, lines $x=1$ and $x=\sqrt{5}$ is $\alpha \sqrt{5}+\beta+\gamma \cos ^{-1}\left(\frac{1}{\sqrt{5}}\right)$, then $|\alpha+\beta+\gamma|$ is equal to $....$
→
Let $A$ be a $3 \times 3$ matrix such that $A^T + 2A= I$ then $det\,(A^{-1}) $ is equal to
→
If the function $f(x)=\left(\frac{1}{x}\right)^{2 x} ; x>0$ attains the maximum value at $x =\frac{1}{ e }$ then :
→
If the points $A(3,{\rm{ }}4),\,B(7,{\rm{ }}7),\,C(a,{\rm{ }}b)$ be collinear and $AC = 10$, then $(a,{\rm{ }}b)$=
→
For $x \in R$, let the function $y(x)$ be the solution of the differential equation$\frac{d y}{d x}+12 y=\cos \left(\frac{\pi}{12} x\right), y(0)=0 .$
Then, which of the following statements is/are TRUE?
→
$\int_{}^{} {{e^x}\sin ({e^x})} \;dx = $
→