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

MCQ

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

A
$0$
B
$1$
C
$2 $
✓
$4$

✓

Answer

Correct option: D.

$4$

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

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

$ = - ( - 2) + (2) = 4$.

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

$\int\frac{\sin^2\text{x}-\cos^2\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{dx}$ is equal to :

$\int\limits^1_0\sqrt{\text{x}(1-\text{x})}\text{ dx}$ equals:

If ${\cos ^{ - 1}}x + {\cos ^{ - 1}}y = 2\pi ,$ then ${\sin ^{ - 1}}x + {\sin ^{ - 1}}y$ is equal to

The lines $\frac{\text{x}}{1}=\frac{\text{y}}{2}=\frac{\text{z}}{3}$ and $\frac{\text{x}-1}{-2}=\frac{\text{y}-2}{-4}=\frac{\text{z}-3}{-6}$ are:

Let the function $f: R \rightarrow R$ be defined by

$f(t)=\left\{\begin{array}{cc}(-1)^{n+1} 2, & \text { if } t=2 n-1, n \in N , \\ \frac{(2 n+1-t)}{2} f(2 n-1)+\frac{(t-(2 n-1))}{2} f(2 n+1), & \text { if } 2 n-1 < t < 2 n+1, n \in N \end{array}\right.$

Define $g(x)=\int_1^x f(t) d t, x \in(1, \infty)$. Let $\alpha$ denote the number of solutions of the equation $g(x)=0$ in the interval $(1,8]$ and $\beta=\lim _{x \rightarrow 1+} \frac{g(x)}{x-1}$. Then the value of $\alpha+\beta$ is equal to. . . . . .

Choose the correct answer from the given four options.
You are given that A and B are two events such that $\text{P}(\text{B})=\frac{3}{5},\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)=\frac{1}{2}$ and $\text{P}(\text{A}\cup\text{B})=\frac{4}{5},$ then P(A) equals:

Let $f(x) = \left\{ {\begin{array}{*{20}{c}} {{x^p}\,\sin \left( {\frac{1}{x}} \right) + x|{x^3}|,\,\,x\, \ne 0}\\{0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0} \end{array}} \right.$ then complete set of values of $p$ for which $f"(x)$ is continuous at $x = 0$ is

Choose the correct answer.The slope of the normal to the curve $y = 2x^2 + 3 \sin x$ at $x = 0$ is:

In a triangle $PQR$, let $\overrightarrow{ a }=\overline{ QR }, \overrightarrow{ b }=\overrightarrow{ RP }$ and $\overrightarrow{ c }=\overline{ PQ }$. If $|\vec{a}|=3,|\vec{b}|=4$ and $\frac{\vec{a} \cdot(\vec{c}-\vec{b})}{\overrightarrow{ c } \cdot(\vec{a}-\vec{b})}=\frac{|\vec{a}|}{|\vec{a}|+|\vec{b}|}$, then the value of $|\vec{a} \times \vec{b}|^2$ is. . . . . . .

Evaluate $\begin{bmatrix}2&5\\-1&-1\end{bmatrix}$