Calculus

Application of Integrals

Medium

The smaller of the areas enclosed by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$ is

$2(\pi - 2)$

$\pi - 2$

$2\pi - 1$

$2\pi + 2$

✅ Correct Option: 2

Circle $x^2+y^2=4$ has radius 2; the line $x+y=2$ passes through $(2,0)$ and $(0,2)$ .

The smaller area is the circular segment cut off by the chord. It equals (quarter-disc area) minus (triangle area):

$\frac{1}{4}\pi(2)^2 - \frac{1}{2}(2)(2) = \pi - 2$ .

2026: 22 May Shift 2

The area (in sq. units) of the region bounded by the line $2y=3x+6$ , x-axis and the ordinates x=-3 and x=1 is:

2025: 22 May Shift 1

The area (in sq. units) bounded by the curve $y = \cos x$ and x-axis between $x = 0$ and $x = \frac{3\pi}{2}$ is

2026: 26 May Shift 2

If the area(in square units) bounded by the curves $y^2 = 4x$ and $y = x$ is $\dfrac{k^3}{3}$ , then the value of $k$ is:

2025: 27 May Shift 1

The marginal cost of production of x units of a commodity is $56 + \frac{3}{2}x$ . It is known that fixed costs are Rs.115. Then the total cost of producing 50 units 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

2025: 21 May Shift 2

Area (in sq. units) of the region bounded by curves $y^2 = x$ and $x = 4$ is

The smaller of the areas enclosed by the circle x2+y2=4x^2 + y^2 = 4x2+y2=4 and the line x+y=2x + y = 2x+y=2 is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The smaller of the areas enclosed by the circle $x^2 + y^2 = 4$ and the line $x + y = 2$ is