Choose the correct answer
The area bounded the curve y = x|x| X- axis and the coordinates x =- 1 and x = 1 is given by
(a) $0$ (b) $\frac{1}{3}$
(c) $\frac{2}{3}$ (d) $\frac{4}{3}$

Open in App

Solution

$G i v e n y = | x | = {\begin{matrix} x^{2}, x \geq 0 - x^{2}, x < 0 \end{matrix}$
Required area = 2 [Area under the curve $y = x^{2}$ , between x = 0, x = 1]
[ $∴$ The curve is symmetrical in opposite quadrant]
$= 2 \int_{0}^{1} x | x | = 2 \int_{0}^{1} x^{2} d x = 2 [\frac{x^{3}}{3}]_{0}^{1} = \frac{2}{3} (1^{3} - 0^{3}) = \frac{2}{3} s q u n i t$
So, the correct option is (c)

Suggest Corrections

Similar questions

Choose the correct answer
Area bounded by the curve $y = x^{3}$ , the X-axis the coordinates x = - 2 and x = 1 si
(a) -9 (b) $- \frac{15}{4}$
(c) $\frac{15}{4}$ (d) $\frac{17}{4}$

Q. The area bounded by the curve

y = x | x |

, X-axis and the coordinates

x = - 1

and

x = 1

is given by

Q. The area bounded by the curve

y = x | x |, x - a x i s

and the ordinates

x = - 1

and

x = 1

is given by

Q. The area bounded between the curve

\frac{x}{4} - \frac{y}{2} + 1

x = - 2, x = 3

and

x

-axis is:

Q. The area bounded by the curve

y = x^{2} + x + 4

, the x-axis and the ordinates

x = 1

and

x = 3

Join BYJU'S Learning Program

Choose the correct answer The area bounded the curve y = x|x| X- axis and the coordinates x =- 1 and x = 1 is given by (a) 0 (b) 13 (c) 23 (d) 43

Given y=|x|={x2,x≥0−x2,x<0 Required area = 2 [Area under the curve y=x2, between x = 0, x = 1] [∴ The curve is symmetrical in opposite quadrant] =2∫10x|x|=2∫10x2dx=2[x33]10=23(13−03)=23sq unit So, the correct option is (c)

Choose the correct answer
The area bounded the curve y = x|x| X- axis and the coordinates x =- 1 and x = 1 is given by
(a) $0$ (b) $\frac{1}{3}$
(c) $\frac{2}{3}$ (d) $\frac{4}{3}$