Download App

Definite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_0^x \frac{x \tan x}{\sec x+\tan x} d x=$
  • A
    $\frac{\pi}{2}-1$
  • B
    $\pi\left(\frac{\pi}{2}+1\right)$
  • C
    $\frac{\pi}{2}+1$
  • ✓
    $\pi\left(\frac{\pi}{2}-1\right)$
✓

Answer

Correct option: D.
$\pi\left(\frac{\pi}{2}-1\right)$
(D)
Let $I =\int_0^\pi \frac{x \tan x}{\sec x+\tan x} d x$ ...(i)
$\therefore \quad I=\int_0^\pi \frac{(\pi-x) \tan x}{\sec x+\tan x} d x$ ...(ii)
$\ldots .\left[\because \int_0^{ a } f (x) d x=\int_0^{ a } f ( a -x) d x\right]$
Adding (i) and (ii), we get
$2 I =\pi \int_0^\pi \frac{\tan x}{\sec x+\tan x} d x$
$\therefore \quad I =\frac{\pi}{2} \int_0^\pi \frac{\sin x}{1+\sin x} d x$
$=\frac{\pi}{2}\left[\int_0^\pi 1 d x-\int_0^\pi \frac{ d x}{1+\sin x}\right]$
On solving, we get
$I=\frac{\pi}{2}(\pi-2)=\pi\left(\frac{\pi}{2}-1\right)$

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 "MCQ" from Definite Integration→Definite Integration — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\int_0^{100 \pi}|\cos x| d x=$ ________.
→
$\cos \left[\tan ^{-1} \frac{1}{3}+\tan ^{-1} \frac{1}{2}\right]=$
→
If $\text{A}=\begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix},$ then $A^5 =$
→
The value of $\tan\Big(\cos^{-1}\frac{3}{5}+\tan^{-1}\frac{1}{4}\Big)=$
→
If the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{\lambda}$ and $\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-5}{5}$ is $\frac{1}{\sqrt{3}}$, the sum of possible value of $\lambda$ is
→
Which of the following is a statement in logic?
→
If $AB = A$ and $BA = B$, where $A$ and $B$ are square matrices, then:
→
If $\triangle A B C$ is right angled at $A$, where $A \equiv(4,2, x)$, $B \equiv(3,1,8)$ and $C \equiv(2,-1,2)$, then the value of $x$ is
→
Select and write the correct alternative from the given option for the questio
The differential equation of $y=A e^{5 x}+B e^{-5 x}$ is
→
Area under the curve $y=\sqrt{3 x+4}$ between $x=0$ and $x=4$ is
→