_0^ x , x x + x ,dx = - Vidyadip

MCQ

$\int_0^\pi {\frac{{x\,\tan x}}{{\sec x + \cos x}}} \,dx = $

✓
$\frac{{{\pi ^2}}}{4}$
B
$\frac{{{\pi ^2}}}{2}$
C
$\frac{{3{\pi ^2}}}{2}$
D
$\frac{{{\pi ^2}}}{3}$

✓

Answer

Correct option: A.

$\frac{{{\pi ^2}}}{4}$

a
(a) Let $I = \int_0^\pi {\frac{{x\tan x}}{{\sec x + \cos x}}dx} = \int_0^\pi {\frac{{(\pi - x)\tan (\pi - x)}}{{\sec (\pi - x) + \cos (\pi - x)}}dx} $

It gives $I = \frac{\pi }{2}\int_0^\pi {\frac{{\sin x}}{{1 + {{\cos }^2}x}}} dx$

Now put $\cos x = t$ and solve, we get

$I = \frac{\pi }{2} \times \frac{\pi }{2} = \frac{{{\pi ^2}}}{4}$.

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 7.2 definite integral→7.2 definite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Let $N$ denote the number that turns up when a fair die is rolled. If the probability that the system of equations

$x+y+z=1$ ; $2 x+N y+2 z=2$ ; $3 x+3 y+N z=3$

has unique solution is $\frac{k}{6}$, then the sum of value of $k$ and all possible values of $N$ is

Let $y=y(x)$ be the solution of the differential equation $x\left(1-x^{2}\right) \frac{d y}{d x}+\left(3 x^{2} y-y-4 x^{3}\right)=0, x>1$ with $y\,(2)=-2$. Then $y\,(3)$ is equal to

Assuming that for a husband-wife couple the chances of their child being a boy or a girl are the same, the probability of their two children being a boy and a girl is

Maximum value of $=\left(\frac{1}{x}\right)^x$:

If $|\vec{a}|=10,|\vec{b}|=2$ and $\vec{a} \cdot \vec{b}=12$, then the value of $|\vec{a} \times \vec{b}|$ is

The equation of the plane parallel to the lines x - 1 = 2y - 5 = 2z and 3x = 4y - 11 = 3z -4 and passing through the point (2, 3, 3) is:

$\left| {\,\begin{array}{*{20}{c}}1&{1 + ac}&{1 + bc}\\1&{1 + ad}&{1 + bd}\\1&{1 + ae}&{1 + be}\end{array}\,} \right| = $

Let $f(x) = \int_{\,1}^{\,x} {\sqrt {2 - {t^2}} dt} $. Then real roots of the equation ${x^2} - f'(x) = 0$ are

Solution of $\int x \sin x d x$ is-

Solve $\int\frac{1}{\sqrt{9-25\text{x}^2}}\text{dx}$

$\frac{1}{5}\sin^{-1}\big(\frac{5\text{x}}{3}\big)+\text{c}$
$\sin^{-1}\big(\frac{5\text{x}}{3}\big)+\text{c}$
$\frac{1}{5}\sin^{-1}\big(\frac{3\text{x}}{3}\big)+\text{c}$
$\sin^{-1}\big(\frac{3\text{x}}{3}\big)+\text{c}$