The value of _1^2 x ,dx is - Vidyadip

MCQ

The value of $\int_1^2 {\log x\,dx} $ is

A
$\log 2/e$
B
$\log 4$
✓
$\log 4/e$
D
$\log 2$

✓

Answer

Correct option: C.

$\log 4/e$

c
(c) $\int_1^2 {\log xdx = [x\log x - x]_1^2 = 2\log 2 - 2 + 1} $

$ = \log 4 - 1 = \log 4 - \log e = \log \frac{4}{e}$.

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 7.2 definite integral→7.2 definite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Choose the correct answer from the given four options.

On using elementary row operation R₁ → R₁ – 3R₂ in the following matrix equation $\begin{bmatrix}4&2\\3&3\end{bmatrix}=\begin{bmatrix}1&2\\0&3\end{bmatrix}\begin{bmatrix}2&0\\1&1\end{bmatrix},$ we have:

$\begin{bmatrix}-5&-7\\3&3\end{bmatrix}=\begin{bmatrix}1&-7\\0&3\end{bmatrix}\begin{bmatrix}2&0\\1&1\end{bmatrix}$
$\begin{bmatrix}-5&-7\\3&3\end{bmatrix}=\begin{bmatrix}1&2\\0&3\end{bmatrix}\begin{bmatrix}-1&-3\\1&1\end{bmatrix}$
$\begin{bmatrix}-5&-7\\3&3\end{bmatrix}=\begin{bmatrix}1&2\\1&-7\end{bmatrix}\begin{bmatrix}2&0\\1&1\end{bmatrix}$
$\begin{bmatrix}4&2\\-5&-7\end{bmatrix}=\begin{bmatrix}1&2\\-3&-3\end{bmatrix}\begin{bmatrix}2&0\\1&1\end{bmatrix}$

Let $\quad \overrightarrow{ a }=\alpha \hat{ i }+3 \hat{ j }-\hat{ k }, \overrightarrow{ b }=3 \hat{ i }-\beta \hat{ j }+4 \hat{ k } \quad$ and $\overrightarrow{ c }=\hat{ i }+2 \hat{ j }-2 \hat{ k }$ where $\alpha, \beta \in R$, be three vectors. If the projection of $\vec{a}$ on $\vec{c}$ is $\frac{10}{3}$ and $\overrightarrow{ b } \times \overrightarrow{ c }=-6 \hat{ i }+10 \hat{ j }+7 \hat{ k }$, then the value of $\alpha+\beta$ equal to

If the lines $x + 2ay + a = 0, x + 3by + b = 0$ and $x + 4cy + c = 0$ are concurrent, then $a, b$ and $c$ are in :-

S is a relation over the set R of all real numbers and it is given by $(\text{a, b})\in\text{S}\Leftrightarrow\text{ab}\geq0.$ Then, S is:

Symmetric and transitive only.
Reflexive and symmetric only.
Antisymmetric relation.
An equivalence relation.

The maximum value of $[x(x-1)+1]^{\frac{1}{3}}, 0 \leq x \leq 1$ is _________.

$[(a \times b) \times (b \times c)\,(b \times c) \times (c \times a)\,(c \times a) \times (a \times b)] = \,$

The number of corner points of the feasible region determined by the constraints $x-y \geq 0,2 y \leq x+2$, $x \geq 0, y \geq 0$ is:

If $f(x) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\sin x}}{x} + \cos x,} \, & \,when \,\, {x \ne 0} \\ {2,} \,& \,\,when\,\,{x = 0} \end{array}} \right.$ then

The vector equation of $X Y$-plane is

If $y = tan x \,\,tan 2x\,\, tan 3x$ then $\frac{{dy}}{{dx}}$ has the value equal to :