Calculus

Application of Integrals

Medium

core

Area bounded by the curves $y = x|x|$ , $x = -1$ , $x = 1$ is

$\frac{1}{3}$ square units

$\frac{2}{3}$ square units

$\frac{1}{6}$ square units

$\frac{1}{2}$ square units

✅ Correct Option: 2

For $x\ge0$ the curve is $y=x^2$ and for $x<0$ it is $y=-x^2$ , so the two pieces are mirror images about the origin. Each encloses area $\int_0^1x^2dx=\frac13$ with the $x$ -axis, and taking the modulus of the negative part the total area is $\frac23$ .

2022: 23 Aug Shift 1

The area bounded by the curve $x^2 = 4y$ and the line $x = 4y - 2$ is :

2026: 31 May Shift 2

Area of the region bounded by the curve $y = \cos x$ and $x-axis$ between $x = 0$ and $x = \pi$ is:

2026: 21 May Shift 2

The area of region $R = \{(x,y): x^2 + y^2 \le 16, y \le \sqrt{3}x, x \ge 0, y \ge 0\}$ is: (in Sq. units)

2025: 27 May Shift 1

The area (in sq.units) of the region enclosed by the curve $y = \cos x$ , $\frac{-\pi}{2} \leq x \leq \frac{\pi}{2}$ and the x - axis is:

2026: 12 May Shift 2

The area of the region bounded by the curves $x^2=4y$ and $x=4y$ is

2026: 18 May Shift 1

The area of the region bounded by curves $y = |x-4|$ , $x = 1$ , $x = 5$ and the x-axis is

Area bounded by the curves y=x∣x∣y = x|x|y=x∣x∣, x=−1x = -1x=−1, x=1x = 1x=1 is

Solution

Related questions:

Keyboard Shortcuts

CUET Mathematics Past Year Questions (Topic-Wise)

Area bounded by the curves $y = x|x|$ , $x = -1$ , $x = 1$ is