Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {u\frac{{{d^2}v}}{{d{x^2}}}dx - \int_{}^{} {v\frac{{{d^2}u}}{{d{x^2}}}dx = } } $
  • ✓
    $u\frac{{dv}}{{dx}} - v\frac{{du}}{{dx}} + c$
  • B
    $2\frac{{du}}{{dx}}\frac{{dv}}{{dx}} + c$
  • C
    $uv + c$
  • D
    $c$
✓

Answer

Correct option: A.
$u\frac{{dv}}{{dx}} - v\frac{{du}}{{dx}} + c$
a
(a) $\int_{}^{} {u\frac{{{d^2}v}}{{d{x^2}}}\,dx} - \int_{}^{} {v\frac{{{d^2}u}}{{d{x^2}}}\,dx} $
$ = u\frac{{dv}}{{dx}} - \int_{}^{} {\frac{{du}}{{dx}}\,.\,\frac{{dv}}{{dx}}\,dx - v\frac{{du}}{{dx}} + \int_{}^{} {\frac{{dv}}{{dx}}\,.\,\frac{{du}}{{dx}}\,dx + c} } $
$ = u\frac{{dv}}{{dx}} - v\frac{{du}}{{dx}} + 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

The value of $c$ so that for all real $x$, the vectors $cxi - 6j + 3k,\,\,xi + 2j + 2cxk$ make an obtuse angle are
→
The differential equation of all parabolas whose axes are parallel to $y$-axis is
→
If $A = \left[ {\begin{array}{*{20}{c}}{{{\cos }^2}\theta }&{\sin \theta \cos \theta }\\{\sin \theta \cos \theta }&{{{\sin }^2}\theta }\end{array}} \right]$, $B = \left[ {\begin{array}{*{20}{c}}{{{\cos }^2}\phi }&{\sin \phi \cos \phi }\\{\sin \phi \cos \phi }&{{{\sin }^2}\phi }\end{array}} \right]$ and $\theta $ and $\phi $ differs by $\frac{\pi }{2},$ then $AB = $
→
If the foot of the perpendicular from point $(4,3,8)$ on the line $L _{1}: \frac{ x - a }{l}=\frac{ y -2}{3}=\frac{ z - b }{4},$ $l \neq 0$ is $(3,5,7),$ then the shortest distance between the line $L _{1}$ and line $L _{2}: \frac{ x -2}{3}=\frac{ y -4}{4}=\frac{ z -5}{5}$ is equal to:
→
Let $f\left( x \right) = {\sin ^4}\,x + {\cos ^4}\,x$. Then $f$ is an increasing function in the interval 
→
$\int_{}^{} {x\sqrt {2x + 3} } \;dx = $
→
Statement $-1$ : The system of linear equations

$x + \left( {\sin \,\alpha } \right)y + \left( {\cos \,\alpha } \right)z = 0$

$x + \left( {\cos \,\alpha } \right)y + \left( {\sin \alpha } \right)z = 0$

$x - \left( {\sin \,\alpha } \right)y - \left( {\cos \alpha } \right)z = 0$

has a non-trivial solution for only one value of $\alpha $ lying in the interval $\left( {0\,,\,\frac{\pi }{2}} \right)$ 

Statement $-2$ : The equation in $\alpha $

$\left| {\begin{array}{*{20}{c}}
  {\cos {\mkern 1mu} \alpha }&{\sin {\mkern 1mu} \alpha }&{\cos {\mkern 1mu} \alpha } \\ 
  {\sin {\mkern 1mu} \alpha }&{\cos {\mkern 1mu} \alpha }&{\sin {\mkern 1mu} \alpha } \\ 
  {\cos {\mkern 1mu} \alpha }&{ - \sin {\mkern 1mu} \alpha }&{ - \cos {\mkern 1mu} \alpha } 
\end{array}} \right| = 0$

has only one solution lying in the interval $\left( {0\,,\,\frac{\pi }{2}} \right)$

→
A box contain 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens draws one by one with replacement at most one is defective?
→
A particle is moving in a straight line. Its displacement at time $t$ is given by $s = - 4{t^2} + 2t$, then its velocity and acceleration at time $t = {1 \over 2}$ second are
→
If $A=\left[\begin{array}{cc}\sin ^2 \theta & \sec ^2 \theta \\ \operatorname{cosec}^2 \theta & \frac{1}{2}\end{array}\right]$ and $B=\left[\begin{array}{cc}\cos ^2 \theta & -\tan ^2 \theta \\ -\cot ^2 \theta & \frac{1}{2}\end{array}\right]$ the value of $A + B$ will be :
→