Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{x^2}\sin 2x} \;dx = $
  • A
    $\frac{1}{2}{x^2}\cos 2x + \frac{1}{2}x\sin 2x + \frac{1}{4}\cos 2x + c$
  • ✓
    $ - \frac{1}{2}{x^2}\cos 2x + \frac{1}{2}x\sin 2x + \frac{1}{4}\cos 2x + c$
  • C
    $\frac{1}{2}{x^2}\cos 2x - \frac{1}{2}x\sin 2x + \frac{1}{4}\cos 2x + c$
  • D
    None of these
✓

Answer

Correct option: B.
$ - \frac{1}{2}{x^2}\cos 2x + \frac{1}{2}x\sin 2x + \frac{1}{4}\cos 2x + c$
b
(b) Let $I = \int_{}^{} {{x^2}\sin 2x\,dx} = \frac{{ - {x^2}\cos 2x}}{2} + \int_{}^{} {\frac{{2x\cos 2x}}{2}\,dx} + c$
$ = - \frac{{{x^2}\cos 2x}}{2} + \frac{{x\sin 2x}}{2} + \frac{{\cos 2x}}{4} + c.$

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 7.1 inderfinite integral→7.1 inderfinite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Which of the following differential equations has $y=c_{1} e^{x}+c_{2} e^{-x}$ as the general solution?
→
Let $A$ and $B$ be any two $n \times n$ matrices such that the following conditions hold: $A B=B A$ and there exist positive integers $k$ and $l$ such that $A^k=I$ ( the identity matrix) and $B^l=0$ (the zero matrix). Then,
→
If $A$ and $B$ are two events such that $P\,(A) \ne 0$ and $P\,(B) \ne 1,$ then $P\left( {\frac{{\overline A }}{{\overline B }}} \right) = $
→
The function $\text{f(x)}=\frac{\text{x}^3+\text{x}^2-16\text{x}+20}{\text{x}-2}$ is not defind for x = 2. in order to make f(x) continuous at x = 2, here f(2) should be defined as:
  1. 0
  2. 1
  3. 2
  4. 3
→
For all real values of  $x$ , increasing function  $f(x)$  is
→
Which of the following functions form Z to itself are bijections?
  1. f(x) = x3
  2. f(x) = x + 2
  3. f(x) = 2x + 1
  4. f(x) = x2 + x
→
Let $|M|$ denote the determinant of a square matrix $M$. Let $g:\left[0, \frac{\pi}{2}\right] \rightarrow R$ be the function defined by

$g(\theta)=\sqrt{f(\theta)-1}+\sqrt{f\left(\frac{\pi}{2}-\theta\right)-1}$

where

$f(\theta)=\frac{1}{2}\left|\begin{array}{ccc}1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1\end{array}\right|+\left|\begin{array}{ccc}\sin \pi & \cos \left(\theta+\frac{\pi}{4}\right) & \tan \left(\theta-\frac{\pi}{4}\right) \\ \sin \left(\theta-\frac{\pi}{4}\right) & -\cos \frac{\pi}{2} & \log _e\left(\frac{4}{\pi}\right) \\ \cot \left(\theta+\frac{\pi}{4}\right) & \log _e\left(\frac{\pi}{4}\right) & \tan \pi\end{array}\right|$.

Let $p (x)$ be a quadratic polynomial whose roots are the maximum and minimum values of the function $g(\theta)$, and $p(2)=2-\sqrt{2}$. Then, which of the following is/are TRUE ?

$(A)$ $p \left(\frac{3+\sqrt{2}}{4}\right)<0$

$(B)$ $p \left(\frac{1+3 \sqrt{2}}{4}\right)>0$

$(C)$ $p \left(\frac{5 \sqrt{2}-1}{4}\right)>0$

$(D)$ $p \left(\frac{5-\sqrt{2}}{4}\right)<0$

→
The solution set of the equation $\tan ^{-1} x-\cot ^{-1} x=\cos ^{-1}(2-x)$ is
→
The value of $\int\limits_0^{\pi /2} {\frac{{{{\sin }^3}\,x}}{{\sin \,x\, + \,\cos \,x}}} \,dx$ is
→
Let $I_n=\int_0^{\pi / 2} x^n \cos x d x$, where $n$ is a non-negative integer. Then, $\sum \limits_{n=2}^{\infty}\left(\frac{I_n}{n !}+\frac{I_n-2}{(n-2) !}\right)$ equals
→