_ , - 1 ^ ,2 |x| ,dx = - Vidyadip

MCQ

$\int_{\, - 1}^{\,2} {|x|\,dx} =$

✓
$5/2$
B
$1/2$
C
$3/2$
D
$7/2$

✓

Answer

Correct option: A.

$5/2$

a
(a) $I = \int_{ - 1}^2 {\,|x|dx} $$ = \int_{ - 1}^0 { - x\,dx} + \int_0^2 {x\,\,dx} $

$ = - \left[ {\frac{{{x^2}}}{2}} \right]_{ - 1}^0 + \left[ {\frac{{{x^2}}}{2}} \right]_0^2$

$ = - \left[ {0 - \frac{1}{2}} \right] + [2]$

$ = 2 + \frac{1}{2} = \frac{5}{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

What are the DRs of vector parallel to (2, -1, 1) and (3, 4, -1):

(1, 5, -2)
(-2, -5, 2)
(-1, 5, 2)
(-1, -5, -2)

The solution of the differential equation $(1 + {x^2})\frac{{dy}}{{dx}} = x$ is

Let $A, B$ and $C$ be three events such that the probability that exactly one of $A$ and $B$ occurs is $(1-k)$, the probability that exactly one of $B$ and $C$ occurs is $(1-2 k)$, the probability that exactly one of $C$ and $A$ occurs is $(1-k)$ and the probability of all $A, B$ and $C$ occur simultaneously is $k^{2}$, where $0\,<\,\mathrm{k}\,<\,1$. Then the probability that at least one of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ occur is:

The points represented by $\vec a,\vec b,\vec c,\vec d$ are coplanar and $\left( {\sin A} \right)\vec a + \left( {2\sin 2B} \right)\vec b + \left( {3\sin 3C} \right)\vec c - 4\vec d = \vec 0$ then the least value of $\frac{{21}}{8}\left( {{{\sin }^2}A + {{\sin }^2}2B + {{\sin }^2}3C} \right)$ is

$\int_0^{\pi /2} {{e^x}\sin x\,dx = } $

If $P$ is a $3 \times 3$ matrix such that $P^{\top}=2 P+I$, where $P^{\top}$ is the transpose of $P$ and $I$ is the $3 \times 3$ identity matrix, then there exists a column matrix $X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right] \neq\left[\begin{array}{l}0 \\ 0 \\ 0\end{array}\right]$ such that

A box is to be made with square base and open top. If the area of material used is $48\,\,$ sq. meter, then maximum volume of the box is ........... $m^3$

If $ a, b, c$ are the position vectors of three collinear points, then the existence of $x, y, z$ is such that

Evaluate: $\int 2^{2^{2^x}} 2^{2^x} 2^x d x$

$\int\frac{\cos2\text{x}-\cos2\theta}{\cos\text{x}-\cos\theta}\text{ dx}$ is equal to:

$2(\sin\text{x}+\text{x}\cos\theta)+\text{C}$
$2(\sin\text{x}-\text{x}\cos\theta)+\text{C}$
$2(\sin\text{x}+2\text{x}\cos\theta)+\text{C}$
$2(\sin\text{x}-2\text{x}\cos\theta)+\text{C}$