Download App

7.1 inderfinite integral — Maths STD 12 Science — Question

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

Answer

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

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

Let $f$ be a continuous, periodic even function defined on $R$ such that $f(0) = 1$, $f(2) = -1$ and period of $f$ is $4$. Minimum number of roots of equation $f(x) = 0$ in $[-10, 10]$ will be
→
How many lines through the origin in make equal angles with the coordinate axis:
→
If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by xRy ⇔ y = 3x, then R =
  1. {(3, 1), (6, 2), (8, 2), (9, 3)}
  2. {(3, 1), (6, 2), (9, 3)}
  3. {(3, 1), (2, 6), (3, 9)}
  4. None of these.
→
The maximum height is reached in $5$ seconds by a stone thrown vertically upwards and moving under the equation  $10s = 10ut -49{t^2}$, where $ s$ is in metre and $t$ is in second. The value of $u$ is ........ $m/\sec $
→
If $f(x) = {\sin ^2}x + {\sin ^2}\left( {x + \frac{\pi }{3}} \right) + \cos x\cos \left( {x + \frac{\pi }{3}} \right)$ and $g\left( {\frac{5}{4}} \right) = 1$, then $(gof)(x) = $
→
Matrix $A=\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 1 & 5 \\ 2 & 4 & 7\end{array}\right]$, then the value of $a_{31} A_{31}+a_{32} A_{32}+a_{33} A_{33}$ is
→
If vectors $(\text{x}-2)\ \vec{\text{a}}+\vec{\text{b}}$ and $(2\text{x}+1)\ \vec{\text{a}}-\vec{\text{b}}$ are parallel then x:
  1. $\frac{1}{3}$
  2. $3$
  3. $-3$
  4. $\frac{-1}{3}$
→
The area bounded by the y-axis, $\text{y}=\cos\text{x}$ and $\text{y}=\sin\text{x}$ when $0\leq\text{x}\leq\frac{\pi}{2}$ is:
  1. $2\big(\sqrt{2}-1\big)$
  2. $\sqrt{2}-1$
  3. $\sqrt{2}+1$
  4. $\sqrt{2}$ 
→
A rectangle has one side on the positive $y-$ axis and one side on the positive $x -$ axis. The upper right hand vertex on the curve $y =\frac{{\ell nx}}{{{x^2}}}$ . The maximum area of the rectangle is
→
If $x=a \sec \theta, y=b \tan \theta$, then $\frac{d^2 y}{d x^2}$ at $\theta=\frac{\pi}{6}$ is
→