_ /4 ^ /2 , cose c ^ 2 ,d = - Vidyadip

MCQ

$\int_{\pi /4}^{\pi /2} {\cos \theta \,{\rm{cose}}{{\rm{c}}^{\rm{2}}}\theta \,d\theta = } $

✓
$\sqrt 2 - 1$
B
$1 - \sqrt 2 $
C
$\sqrt 2 + 1$
D
None of these

✓

Answer

Correct option: A.

$\sqrt 2 - 1$

a
(a) Let $\int_{\pi /4}^{\pi /2} {\cos \theta \frac{1}{{{{\sin }^2}\theta }}d\theta } $

Put $t = \sin \theta \Rightarrow dt = \cos \theta \,\,d\theta ,$

then we have

$\int_{1/\sqrt 2 }^1 {\frac{1}{{{t^2}}}dt} = \left[ {\frac{{ - 1}}{t}} \right]_{1/\sqrt 2 }^1 $

$= \sqrt 2 - 1$.

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

If the sum of the first $11$ terms of the series ${\left( {1\frac{4}{7}} \right)^2} + {\left( {1\frac{5}{7}} \right)^2} + {\left( {1\frac{6}{7}} \right)^2} + {2^2} + {\left( {2\frac{1}{7}} \right)^2} + ......$ is $\frac{{11}}{7}\lambda $ then $\lambda $ is equal to

Force $3i + 2j + 5k$ and $2i + j - 3k$ are acting on a particle and displace it from the point $2i - j - 3k$ to the point $4i - 3j + 7k,$ then work done by the force is ............... $\mathrm{unit}$

Let $\vec{a}=3 \hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{ c }=2 \hat{ i }-3 \hat{ j }+3 \hat{k}$. If $\vec{b}$ is $a$ vector such that $\vec{a}=\vec{b} \times \vec{c}$ and $|\vec{b}|^2=50$, then $|72-| \vec{b}+\left.\vec{c}\right|^2 \mid$ is equal to $..........$.

The domain of ${\sin ^{ - 1}}\left[ {{{\log }_3}\left( {\frac{x}{3}} \right)} \right]$ is

From which of the following the distance of the point $(1,\,\,2,\,\,3)$ is $\sqrt {10} $

Let $\alpha, \beta(\alpha>\beta)$ be the roots of the quadratic equation $x ^{2}- x -4=0$. If $P _{ a }=\alpha^{ n }-\beta^{ n }, n \in N$, then $\frac{ P _{15} P _{16}- P _{14} P _{16}- P _{15}^{2}+ P _{14} P _{15}}{ P _{13} P _{14}}$ is equal to$......$

A drawer contains $5$ brown socks and $4$ blue socks well mixed. A man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match

The number of integral values of $m$ for which the equation $(1 + m^2) x^2 - 2(1 + 3m) x + (1 + 8m) = 0$ has no real root is

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

$\int_0^1 {\frac{{{{\tan }^{ - 1}}x}}{{1 + {x^2}}}} \,dx = $