If f(x) is a quadratic in x , then _0^1 f(x) dx is - Vidyadip

MCQ

If $f(x)$ is a quadratic in $x$ , then $\int\limits_0^1 {f(x) dx}$ is

✓
$\frac{1}{6}\left( {f\left( 0 \right) + 4f\left( {\frac{1}{2}} \right) + f(1)} \right)$
B
$\frac{1}{6}\left( {4f\left( 0 \right) + f\left( {\frac{1}{2}} \right) + f(1)} \right)$
C
$\frac{1}{6}\left( {f\left( 0 \right) + f\left( {\frac{1}{2}} \right) + 4f(1)} \right)$
D
$\frac{1}{6}\left( {f\left( 0 \right) + f\left( {\frac{1}{2}} \right) + f(1)} \right)$

✓

Answer

Correct option: A.

$\frac{1}{6}\left( {f\left( 0 \right) + 4f\left( {\frac{1}{2}} \right) + f(1)} \right)$

a
If $f(x)=a x^{2}+b x+c$

$\int_{0}^{1} f(x) d x=\frac{1}{6}(2 a+3 b+6 c)$

$f(0)=c, f\left(\frac{1}{2}\right)=\frac{a}{4}+\frac{b}{2}+c$

$f(1)=a+b+c$

$\Rightarrow f(0)+4 f\left(\frac{1}{2}\right)+f(1)=2 \mathrm{a}+3 \mathrm{b}+6 \mathrm{c}$

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

$\smallint \frac{{dx}}{{\cos x + \sqrt 3 \sin x}} = $

For some $a, b, c \in N$, let $f(x)=a x-3$ and $g ( x )= x ^{ b }+ c , x \in R$. If $(\text { fog })^{-1}( x )=\left(\frac{ x -7}{2}\right)^{1 / 3}$ then $(fog) (ac) + (gof) (b)$ is equal to $..........$

The area bounded by curves $y = \cos x$ and $y = \sin x$ and ordinates $x = 0$ and $x = \frac{\pi }{4}$ is

Solve $\int\frac{1}{\sqrt{9-25\text{x}^2}}\text{dx}$

If $m$ and $n$ respectively are the number of local maximum and local minimum points of the function $f ( x )=\int_{0}^{ x ^{2}} \frac{ t ^{2}-5 t +4}{2+ e ^{ t }} dt$, then the ordered pair $( m , n )$ is equal to

Let a unit vector which makes an angle of $60^{\circ}$ with $2 \hat{i}+2 \hat{j}-\hat{k}$ and an angle of $45^{\circ}$ with $\hat{i}-\hat{k}$ be $\overrightarrow{\mathrm{C}}$. Then $\overrightarrow{\mathrm{C}}+\left(-\frac{1}{2} \hat{\mathrm{i}}+\frac{1}{3 \sqrt{2}} \hat{\mathrm{j}}-\frac{\sqrt{2}}{3} \hat{\mathrm{k}}\right)$ is :

In a binomial distribution $B(n\,\,,\,p =$ $\frac{1}{4}$) ,if the probability of at least one success is greater than or equal to$ \frac{9}{{10}}$ then $n$ greater than :

If x > 1, then $2\tan^{-1}\text{x}+\sin^{-1}\Big(\frac{2\text{x}}{1+\text{x}^2}\Big)$ is equal to:

Area between the parabolas $y^2=4 a x$ and $x^2=4 a y$ is:

The solution of the differential equation $\text{x}\frac{\text{dy}}{\text{dx}}=\text{y}+\text{x}\ \tan\frac{\text{y}}{\text{x}}$ is :