Calculus

Application of Integrals

Easy

core

The area bounded by the line $y=x$ , the $x-axis$ and the ordinates $x=-1$ and $x=2$ is

$\frac{3}{2}$ Sq.units

$\frac{5}{2}$ Sq.units

$\frac{7}{2}$ Sq.units

$\frac{9}{2}$ Sq.units

✅ Correct Option: 2

The line lies below the axis on $[-1,0]$ and above on $[0,2]$ , so take absolute values.

Area $=\int_{-1}^{0}(-x)dx+\int_0^2 x\,dx=\frac{1}{2}+2=\frac{5}{2}$ square units.

2026: 29 May Shift 2

Area bounded by the curves $y=x^3$ , $y=x+6$ and $x=0$ is

2022: 7 Aug Shift 2

The area of the region bounded by $f(x) = x|x|$ and x-axis from $x = 0$ to $x = 4$ is :

2025: 13 May Shift 1

The area (in sq. units) of the region bounded by the curve $y = 2x^3$ , $x$ - axis and ordinates $x = -1$ and $x = 1$ is:

2025: 30 May Shift 1

The area (in sq. units) of the region in the first quadrant bounded by $y = 3\sqrt{1-x^2}$ , $x \in [0,1]$ and the x-axis is equal to

2025: 22 May Shift 1

The area (in sq. units) of the region bounded by the curve $y = \sqrt{16-x^2}$ and x-axis is

2026: 30 May Shift 2

The area bounded by the curve $y^2 = 2x$ , $y$ -axis and the line $y=1$ , is

The area bounded by the line y=xy=xy=x, the x−axisx-axisx−axis and the ordinates x=−1x=-1x=−1 and x=2x=2x=2 is