The value of 12 _0^3 |x^2-3 x+2 | d x is ............. - Vidyadip

MCQ

The value of $12 \int \limits_0^3\left|x^2-3 x+2\right| d x$ is $.............$

A
$20$
B
$25$
✓
$22$
D
$65$

✓

Answer

Correct option: C.

$22$

c
$12 \int \limits_0^3\left| x ^2-3 x +2\right| dx$

$={ }_{12} \int_0^3\left|\left( x -\frac{3}{2}\right)^2-\frac{1}{4}\right| dx$

If $x-\frac{3}{2}=t$

$dx = dt$

$=24 \int \limits_0^{3 / 2}\left| t ^2-\frac{1}{4}\right| dt$

$=24\left[-\int^{1 / 2}\left(t^2-\frac{1}{4}\right) d t+\int \limits_0^{3 / 2}\left(t^2-\frac{1}{4}\right) d t\right]=22$

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

The angle between the lines whose direction cosines are connected by the relations $l + m + n = 0$ and $2lm + 2nl - mn = 0$, is

Let $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ be three unit vectors, such that $\big|\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}\big|=1$ and $\vec{\text{a}}$ is perpendicular to $\vec{\text{b}}.$ If $\vec{\text{c}}$ makes angle $\alpha$ and $\beta$ with $\vec{\text{a}}$ and $\vec{\text{b}}$ respectively, then $\cos\alpha+\cos\beta=$

$-\frac{3}{2}$
$\frac{3}{2}$
$1$
$-1$

If two vertices of a triangle are $i - j$ and $j + k$, then the third vertex can be

If $\text{f}\text{(x)}=\sqrt{\text{x}^2-10\text{x}+25},$ then the derivative of f(x) in the intereval [0, 7] is:

1
-1
0
None of these.

The area of the region bounded by the curve $y=x|x|$, lines $x=-1$ and $x=1$ is, __________ .

If $\text{A}=\begin{bmatrix}2&0&-3\\4&3&1\\-5&7&2\end{bmatrix}$ is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is:

$\begin{bmatrix}2&2&-4\\2&3&4\\-4&4&2\end{bmatrix}$
$\begin{bmatrix}2&4&-5\\0&3&7\\-3&1&2\end{bmatrix}$
$\begin{bmatrix}4&4&-8\\4&6&8\\-8&8&4\end{bmatrix}$
$\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$

$\int {} $ $e^{\tan \theta} $ $(\sec \theta - \sin \theta )$ $ d\theta $ equals :

If $\int {\frac{{{x^2} - x + 1}}{{{x^2} + 1}}{e^{{{\cot }^{ - 1}}}}{}^x\,dx = A(x)} {e^{{{\cot }^{ - 1}}}}{}^x + C,$ then $A(x)$ is equal to

Two differentiable functions $f(x)$ and $g(x)$ are such that $f$"$(x) > 0$ and $g$"$(x) < 0$$\forall x \in (a,b)$ and $\int\limits_a^b {f(x)dx\, = } \,\int\limits_a^b g(x)dx\,.\,$ If $f(x) = g(x)$ for $x\,=\,\alpha ,\beta \in (a,b)(\alpha < \beta ),\,$ , then

The angle between the lines whose direction cosines are proportional to $(1, 2, 1)$ and $(2, -3, 6)$ is