Download App

7.2 definite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.2 definite integral1 Mark
MCQ
$\int\limits_a^b {} \, [x] \,dx + \int\limits_a^b {} \, [ - x] \,dx$

where $[. ]$ denotes greatest integer function is equal to :

  • A
    $a + b$
  • B
    $b - a$
  • ✓
    $a - b$
  • D
    $\frac{{a\, + \,b}}{2}$
✓

Answer

Correct option: C.
$a - b$
c
$[x] + [- x] = \left[ {\begin{array}{*{20}{c}}{0\,\,\,\,if\,\,\,\,x\,\, \in \,\,I\,\,\,}\\{ - \,1\,\,\,\,if\,\,\,\,x\,\, \notin \,\,I}\end{array}} \right.$

$\Rightarrow$ $I = \int\limits_a^b {}  - dx = a - b$

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

If $P $ and  $ Q $ be the middle points of the sides $BC$  and $ CD$  of the parallelogram $ABCD$ , then $\overrightarrow {AP} + \overrightarrow {AQ} = $
→
Ramkali is trying to find the solution of the following definite integrals :
(i) $\int_0^{2 \pi} \frac{d x}{e^{\sin x}+1}$
(ii) $\int_0^1 x^2 d x$
(iii) $\int_0^1 e^x d x$
Which of the above integrals solved by using of definite integral properties?
→
If $\text{A}=\begin{bmatrix}3&\text{x}-1\\2\text{x}+3&\text{x}+2\end{bmatrix}$ is a symmetric matrix, then x =
  1. 4
  2. 3
  3. -4
  4. -3
→
The solution of the equation $\frac{{dy}}{{dx}} = \frac{{x + y}}{{x - y}}$ is
→
If the function $f(x) = {{K\sin x + 2\cos x} \over {\sin x + \cos x}}$ is increasing for all values of $x,$ then
→
Area bounded by the lines $y = x,\,\,x = - 1,\,\,x = 2$ and $x - $ axis is
→
If $A$  is a square matrix $A + {A^T}$ is symmetric matrix, then $A - {A^T}$=
→
If $\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}=4 \hat{i}+4 \hat{j}-2 \hat{k}$ then find the angle between the vectors $\vec{a}$ and $\vec{b}$.
→
If P(E) = 0.35 and $P(E \cup F)$ = 0.6 and E and F are independent events, then P(F) is equal to -
→
An experiment succeeds twice as often as it fails. The probability of at least $5$ successes in the six trials of this experiment is
→