_ , - 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 STD 12 - 7.2 definite integral→STD 12 - 7.2 definite integral — all question types→Mathematics STD 12 Science question papers→CBSE Board STD 12 Science question papers→CBSE Board question paper generator→

Similar questions

Choose the correct answer in Exercise:
$\int\frac{\text{dx}}{\text{x}^2+2\text{x}+2}\text{equals}$

The maximum value of $Z = 4x + 3y$ subjected to the constraints $3x + 2y \geq 160, 5x + 2y \geq 200, x + 2y \geq 80, x, y \geq 0$ is :

The unit vector perpendicular to the vectors $6i + 2j + 3k$ and $3i - 6j - 2k,$ is

There are three bags $B_1, B_2$ and $B_3$. The bag $B_1$ contains $5$ red and $5$ green balls, $B_2$ contains $3$ red and 5 green balls, and $B_3$ contains $5$ red and $3$ green balls, Bags $B_1, B_2$ and $B_3$ have probabilities $\frac{3}{10}, \frac{3}{10}$ and $\frac{4}{10}$ respectively of being chosen. A bag is selected at random and a ball is chosen at random from the bag. Then which of the following options is/are correct?

$(1)$ Probability that the selected bag is $B _3$ and the chosen ball is green equals $\frac{3}{10}$

$(2)$ Probability that the chosen ball is green equals $\frac{39}{80}$

$(3)$ Probability that the chosen ball is green, given that the selected bag is $B_3$, equals $\frac{3}{8}$

$(4)$ Probability that the selected bag is $B_3$, given that the chosen balls is green, equals $\frac{5}{13}$

The direction cosines of $z$ axis are

Let $f'(x) > 0$ and $g'(x) < 0$ for all $x \in R$ then

If $A = \left[ {\begin{array}{*{20}{c}}
1&0&0 \\
2&1&0 \\
{ - 3}&2&1
\end{array}} \right]\,$ and $B = \left[ {\begin{array}{*{20}{c}}
1&0&0 \\
{ - 2}&1&0 \\
7&{ - 2}&1
\end{array}} \right]$ then $AB$ equals

The binary operation $*$ defined on $N$ by $a^ * b = a + b + ab$ for all $a, b \in N$ is:

The degree of the differential equation $\text{y}_3^\frac{2}{3}+2+3\text{y}_2+\text{y}_1=0$ is:

If $A=\left[\begin{array}{lll}1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1\end{array}\right]$, then $A^2=$ ?