Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int_1^2 {\frac{{\cos (\log x)}}{x}} \,dx = $
  • A
    $\sin \,(\log 3)$
  • ✓
    $\sin \,(\log 2)$
  • C
    $\cos \,(\log 3)$
  • D
    None of these
✓

Answer

Correct option: B.
$\sin \,(\log 2)$
b
(b) Put $t = \log x \Rightarrow dt = \frac{1}{x}dx$.

As $x = 2 \Rightarrow t = \log 2$

and $x = 1 \Rightarrow t = 0$, we have

$\int_1^2 {\frac{{\cos (\log x)}}{x}} dx = - \int_0^{\log 2} {\cos t\,dt} = [\sin t]_0^{\log 2}$$ = \sin (\log 2)$.

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

${d \over {dx}}\left( {{{\tan }^{ - 1}}\sqrt {{{1 + \cos {x \over 2}} \over {1 - \cos {x \over 2}}}} } \right)$ is equal to
→
Let $f:(0,1) \rightarrow R$ be the function defined as $f(x)=[4 x]\left(x-\frac{1}{4}\right)^2\left(x-\frac{1}{2}\right)$, where $[x]$ denotes the greatest integer less than or equal to $x$. Then which of the following statements is(are) true?

($A$) The function $f$ is discontinuous exactly at one point in $(0,1)$

($B$) There is exactly one point in $(0,1)$ at which the function $f$ is continuous but $NOT$ differentiable

($C$) The function $\mathrm{f}$ is $NOT$ differentiable at more than three points in $(0,1)$

($D$) The minimum value of the function $f$ is $-\frac{1}{512}$

→
If A is a matrix of order m×n and B is a matrix such that ABT and BTA are both defined, then the order of matrix B is:
  1. m×n
  2. n×n
  3. n×m
  4. m×n
→
Let $a, b, c, d$ be in arithmetic progression with common difference $\lambda$. If

$\left|\begin{array}{lll} x+a-c & x+b & x+a \\ x-1 & x+c & x+b \\ x-b+d & x+d & x+c \end{array}\right|=2$

then value of $\lambda^{2}$ is equal to $.....$

→
If $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ are three non-zero vectors, no two of which are collinear and the vector $\vec{\text{a}}+\vec{\text{b}}$ is collinear with $\vec{\text{c}}$, $\vec{\text{b}}+\vec{\text{c}}$ is collinear with $\vec{\text{a}}$, then $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}=$
  1. $\vec{\text{a}}$
  2. $\vec{\text{b}}$
  3. $\vec{\text{c}}$
  4. None of these
→
Let $f(x)=x^3+a x^2+b x+c$ where $a, b, c$ are real numbers. If $f(x)$ has a local minimum at $x=1$ and a local maximum at $x=-\frac{1}{3}$ and $f(2)=0$, then $\int_{-1}^1 f(x) d x$ equals
→
Let $S=\{1,2,3,4\}$. Then the number of elements in the set $\{f: S \times S \rightarrow S: f$ is onto and $f(a, b)=f(b, a)$ $\geq a; \forall(a, b) \in S \times S\}$ is
→
A unit vector perpendicular to vector  $  c $ and coplanar with vectors  $a$  and $b$ is
→
The given table shows the number of cars manufactured in four different colours on a particular day. Study it carefully and answer the question.
 
Number of cars manufactured
Colour
Vento
Creta
WagonR
Red
65
88
93
White
54
42
80
Black
66
52
88
Sliver
37
49
74
What was the total number of black cars manufactured?
→
If $e^x+e^y=e^{x+y}$, then $\frac{d y}{d x}$ is
→