_0^ /2 x x ,dx equals - Vidyadip

MCQ

$\int_0^{\pi /2} {x\cot x\,dx} $ equals

A
$ - \frac{\pi }{2}\log 2$
✓
$\frac{\pi }{2}\log 2$
C
$\pi \log 2$
D
$ - \pi \log 2$

✓

Answer

Correct option: B.

$\frac{\pi }{2}\log 2$

b
(b) $I = \int_0^{\pi /2} {x\cot x\,dx} $

Integrating by parts, we get

$[x(\log \sin x)]_0^{\pi /2} - \int_0^{\pi /2} {\log \sin x\,dx} $

$I = - \left( { - \frac{\pi }{2}\log 2} \right) = \frac{\pi }{2}\log 2$.

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

Let ${a_1},{a_2},{a_3}, \ldots $ be terms of $A.P.$ If $\frac{{{a_1} + {a_2} + \ldots + {a_p}}}{{{a_1} + {a_2} + \ldots + {a_q}}} = \frac{{{p^2}}}{{{q^2}}},p \ne q$ then $\frac{{{a_6}}}{{{a_{21}}}}$ equals

If $a = i + j + k,\,\,b = 4i + 3j + 4k$ and $c = i + \alpha j + \beta k$ are linearly dependent vectors and $|c| = \sqrt 3 ,$ then

Let $z _{1}$ and $z _{2}$ be two complex numbers such that $\overline{ z }_{1}=i \overline{ z }_{2}$ and $\arg \left(\frac{ z _{1}}{\overline{ z }_{2}}\right)=\pi$. Then

$\mathop {\lim }\limits_{x \to - 2} \frac{{{{\sin }^{ - 1}}(x + 2)}}{{{x^2} + 2x}}$ is equal to

$\int_{ - \pi /4}^{\pi /2} {{e^{ - x}}\sin x\,dx} = $

Consider three observations $a, b$ and $c$ such that $b = a + c .$ If the standard deviation of $a +2$ $b +2, c +2$ is $d ,$ then which of the following is true ?

Let $A$ and $B$ be two non -null events such that $A \subset B$. Then, which of the following statements is always correct?

Domain of the function $f(x)\,=\,\frac{1}{{\sqrt {(x + 1)({e^x} - 1)(x - 4)(x + 5)(x - 6)} }}$

The equation ${x^{(3/4){{({{\log }_2}x)}^2} + ({{\log }_2}x) - 5/4}} = \sqrt 2 $ has

The exact value of $\cos \frac{{2\pi }}{{28}}\,\cos ec\frac{{3\pi }}{{28}}\, + \,\cos \frac{{6\pi }}{{28}}\,\cos ec\frac{{9\pi }}{{28}} + \cos \frac{{18\pi }}{{28}}\cos ec\frac{{27\pi }}{{28}}$ is equal to