Area bounded between the curve x^2=y and the line y=4 x is: - Vidyadip

MCQ

Area bounded between the curve $x^2=y$ and the line $y=4 x$ is:

✓
$\frac{32}{3}\text{sq}$ unit
B
$\frac{1}{3}\text{sq}$ unit
C
$\frac{8}{3}\text{sq}$ unit
D
$\frac{16}{3}\text{sq}$ unit

✓

Answer

Correct option: A.

$\frac{32}{3}\text{sq}$ unit

Given curves are $x^2=y$ and $y=4 x$
Intersection points are $(0, 0)$ and $(4, 16)$
$\therefore$ Required area
$=\int\limits^4_0(4\text{x}-\text{x}^2)\text{dx}$
$=\Big[\frac{4\text{x}^2}{2}-\frac{\text{x}^3}{3}\Big]^4_0$
$=\Big[32-\frac{64}{3}\Big]$
$=\frac{32}{3}\text{sq}$ unit

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 Application of Integrals→Application of Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^2=x \sin \frac{d y}{d x}$ is

The function $f: R \rightarrow R$ defined by $f(x)=4+3 \cos x$ is

The range of the function $f(x)=(\sin x)^{\sin x}$ defined on $(0, \pi)$ is

Minimize $Z = 20x_1 + 9x_2$, subject to $\text{x}_{1}\geq0,\text{x}_{2}\geq0,2\text{x}_{1}+2\text{x}_{2}\geq36,6\text{x}_{1}+\text{x}_{2}\geq60.$

Let ${\tan ^{ - 1}}\left( {\tan \frac{{5\pi }}{4}} \right) = \alpha ,{\tan ^{ - 1}}\left( { - \tan \frac{{2\pi }}{3}} \right) = \beta $ Then :-

The area of the region bounded by the curve $y = x^3,$ and the lines, $y = 8,$ and $x = 0,$ is

Which of the following functions is not one-one?

Area of triangle whose two vertices formed from the $x-$axis and line $y = 3 - |x|$ is:

The line $y = mx$ bisects the area enclosed by lines $\text{x}=0,\text{y}=0$ and $\text{x}=\frac{3}{2}$ and the curve $\text{y}=1+4\text{x}-\text{x}^2.$ Then the value of $m$ is:

$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $ are non coplanar vectors such that $\overrightarrow P = \overrightarrow a + \overrightarrow b + \overrightarrow c, \overrightarrow Q = 4 \overrightarrow a + 3 \overrightarrow b + 4 \overrightarrow c$ and $ \overrightarrow R = \overrightarrow a + \alpha \overrightarrow b + \beta \overrightarrow c $ are linearly dependent vectors, then number of possible values of $\alpha$ is