_ ^ u d^2 v d x^2 dx - _ ^ v d^2 u d x^2 dx = - Vidyadip

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

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

A line is such that its segment between the straight lines $5x - y - 4 = 0$ and $3x + 4y - 4 = 0$ is bisected at the point $(1, 5)$, then its equation is

Let $A=\left[a_{i j}\right]_{2 \times 2}$ where $a_{i j} \neq 0$ for all $i, j$ and $A^2=I$. Let a be the sum of all diagonal elements of $A$ and $b =| A |$, then $3 a ^2+4 b ^2$ is equal to

The sum of the coefficient of $x^{2 / 3}$ and $x^{-2 / 5}$ in the binomial expansion of $\left(x^{2 / 3}+\frac{1}{2} x^{-2 / 5}\right)^9$ is :

The maximum value of $( 7 \,cos\theta + 24\, sin\theta ) × ( 7\, sin\theta - 24\, cos\theta)$ for every $\theta \,\, \in \,\,R$.

Sum of first $n$ terms of a sequence is given by $S_0 = 3n^2 + 4n + 15$ If $T_r$ is $r^{th}$ term of sequence, then $T_3 - T_1$ is equal to

$\int_{}^{} {\frac{{\cos 2x}}{{{{(\cos x + \sin x)}^2}}}\;dx = } $

Mean deviation is least if it is taken about :-

If the mean of $3, 4, x, 7, 10$ is $6$, then the value of $x$ is

If $A + B + C = \pi ,$ then ${\tan ^2}\frac{A}{2} + {\tan ^2}\frac{B}{2} + $${\tan ^2}\frac{C}{2}$ is always

The sum of first $20$ terms of the sequence $0.7,0.77,0.777, . . . $ is