Calculus

Application of Integrals

Medium

The line $y = x$ , partition the area of the circle $(x-1)^2 + y^2 = 1$ , into two segments. The area of the major segment is

$\frac{\pi}{2} + \frac{1}{4}$

$\frac{\pi}{4} + \frac{1}{2}$

$\frac{3\pi}{4} + \frac{1}{6}$

$\frac{3\pi}{4} + \frac{1}{2}$

✅ Correct Option: 4

Circle has centre $(1,0)$ , radius 1. Line $y=x$ passes through $(0,0)$ and $(1,1)$ , both on the circle. The chord subtends a $90^\circ$ angle at the centre. Minor segment area $=$ sector area $-$ triangle area $= \frac{\pi}{4} - \frac{1}{2}$ . Major segment area $= \pi(1)^2 - (\frac{\pi}{4} - \frac{1}{2}) = \frac{3\pi}{4} + \frac{1}{2}$ .

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Area (in sq. units) of the region bounded by the curves $y = -1$ , $y = 2$ , $x = y^3$ and $x = 0$ is

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

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Area of the region bounded by $y = -1$ , $y = 2$ , $x = y^3$ and $x = 0$ is :

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

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The area of region $\{(x,y): 9x^2+16y^2\le144, x\ge0, y\ge0\}$ is-

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The area of the shaded portion is :

The line y=xy = xy=x, partition the area of the circle (x−1)2+y2=1(x-1)^2 + y^2 = 1(x−1)2+y2=1, into two segments. The area of the major segment is

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The line $y = x$ , partition the area of the circle $(x-1)^2 + y^2 = 1$ , into two segments. The area of the major segment is