_ /4 ^ 3 /4 dx 1 + x is equal to - Vidyadip

MCQ

$\int\limits_{\pi /4}^{3\pi /4} {\frac{{dx}}{{1 + \cos x}}} $ is equal to

✓
$2$
B
$ - 2$
C
$\frac{1}{2}$
D
$ - \frac{1}{2}$

✓

Answer

Correct option: A.

$2$

a
(a) $\int_{\pi /4}^{3\pi /4} {\frac{{dx}}{{1 + \cos x}}} $

$\int_{\pi /4}^{3\pi /4} {\frac{{1 - \cos x}}{{1 - {{\cos }^2}x}}} \,dx = \int_{\pi /4}^{3\pi /4} {\frac{{1 - \cos x}}{{{{\sin }^2}x}}} \,dx$

$ = \int_{\pi /4}^{3\pi /4} {({\rm{cose}}{{\rm{c}}^2}x} - \cot x{\rm{cosec}}\,x)\,dx$

$ = \,( - \cot x + {\rm{cosec}}\,x{\rm{)}}_{\pi {\rm{/4}}}^{{\rm{3}}\pi {\rm{/4}}} = 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

More "M.C.Q (1 Marks)" from STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Let $\vec{a}$ be a vector which is perpendicular to the vector $3 \hat{ i }+\frac{1}{2} \hat{ j }+2 \hat{ k }$. If $\overrightarrow{ a } \times(2 \hat{ i }+\hat{ k })=2 \hat{ i }-13 \hat{ j }-4 \hat{ k }$, then the projection of the vector $\vec{a}$ on the vector $2 \hat{ i }+2 \hat{ j }+\hat{ k }$ is

The sum of three numbers is $6 .$ If we multiply third number by $3$ and add second number to it, we get $11$. By adding first and third numbers, we get double of the second number. Represent it algebraically and find the numbers using matrix method.

Let $A, B$ and $C$ be three events, which are pair-wise independence and $\bar E$ denotes the complement of an event $E$ . If $P(A \cap B \cap C) = 0$ and $P(C) > 0,$ then $P[(\bar A \cap \bar B)|\,C]$ is equal to

If $ b$ and $c$ are any two non-collinear unit vectors and $a$ is any vector, then $(a\,.\,b)\,b + (a\,.\,c)\,c + \frac{{a\,.\,(b \times c)}}{{|b \times c|}}\,(b \times c) = $

If ${e^{f(x)}} = \frac{{10 + x}}{{10 - x}},\;x \in ( - 10,\;10)$ and $f(x) = kf\left( {\frac{{200x}}{{100 + {x^2}}}} \right)$, then $k = $

If $A=\left[\begin{array}{ll}0 & 2 \\ 2 & 0\end{array}\right]$, then $A^2$ is equal to

A unit vector which is coplanar to vector and $i + 2j + k$ and $i + 2j + k$ and perpendicular to $i + j + k,$ is

If the function $\text{f}(\text{x})=\frac{-\text{x}}{2}+\sin\text{x}$ defined on $\Big[\frac{-\pi}{3},\frac{\pi}{3}\Big]$ is:

Choose the correct answer from the given four options:The area of the region bounded by the $y-$axis, $\text{y}=\cos\text{x}$ and $\text{y}=\sin\text{x},0\leq\text{x}\leq\frac{\pi}{2}$ is:

The optimal value of the objective function is attained at the points: