Area Under The Curves - Calculus - Mathematics Previous Year Questions

1

2020 · Mathematics · Calculus · Area Under The Curves

COMEDK 2020

The area bounded by the curve \(x=4-y^2\) and the Y-axis is

A

32 sq units

B

16 sq units

C

\(\frac{16}{3}\) sq units

D

\(\frac{32}{3}\) sq units

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2

2020 · Mathematics · Calculus · Area Under The Curves

COMEDK 2020

The area enclosed by the pair of lines \(xy=0\), the line \(x-4=0\) and \(y+5=0\) is

A

10 sq units

B

20 sq units

C

0 sq units

D

\(\frac{5}{4}\) sq units

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3

2023 · Mathematics · Calculus · Area Under The Curves

COMEDK 2023 EVENING SHIFT

The area bounded by the curve \(y^2=4 a^2(x-1)\) and the lines \(x=1, y=4 a\) is

A

\(\frac{16}{3} a \text { sq units }\)

B

\(\frac{16}{3} a^2 \text { squnits }\)

C

\(16 a^2 \text { squnits }\)

D

\(4 a^2 \text { sq units }\)

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4

2023 · Mathematics · Calculus · Area Under The Curves

COMEDK 2023 EVENING SHIFT

The area of the upper half of the circle whose equation is \((x-1)^2+y^2=1\) is given by

A

\(\frac{\pi}{4} \text { sq units }\)

B

\(\int_\limits0^2 \sqrt{2-x^2} d x \text { sq units }\)

C

\(\int_\limits0^2 \sqrt{2x-x^2} d x \text { sq units }\)

D

\(\int_\limits0^1 \sqrt{2x-x^2} d x \text { sq units }\)

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5

2024 · Mathematics · Calculus · Area Under The Curves

COMEDK 2024 AFTERNOON SHIFT

$$\text { The area of the region (in square units) bounded by the line } y+3=x ; x=1 \text { and } x=5 \text { is }$$

A

2

B

32

C

24

D

4

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6

2024 · Mathematics · Calculus · Area Under The Curves

COMEDK 2024 AFTERNOON SHIFT

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

A

20\(\pi\)

B

16\(\pi\)

C

256\(\pi\)

D

8\(\pi\)

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7

2024 · Mathematics · Calculus · Area Under The Curves

COMEDK 2024 EVENING SHIFT

The area bounded by the curve \(y=\cos x, x=0\) and \(x=\pi\) is

A

2 sq units

B

1 sq units

C

4 sq units

D

3 sq units

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8

2025 · Mathematics · Calculus · Area Under The Curves

COMEDK 2025 AFTERNOON SHIFT

The area of the region enclosed by the lines $2 x+y=10, y=1, y=5$ and the $y$-axis is

A

28 sq units

B

9.5 sq units

C

14 sq units

D

37.5 sq units

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9

2025 · Mathematics · Calculus · Area Under The Curves

COMEDK 2025 EVENING SHIFT

Area of the region bounded by the curve $y=\cos x$ between $x=-\frac{\pi}{2}$ and $x=\pi$ is ------------------

A

3 sq units

B

4 sq units

C

1 sq units

D

2 sq units

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10

2025 · Mathematics · Calculus · Area Under The Curves

COMEDK 2025 EVENING SHIFT

If the area under the curve $y=\sqrt{a^2-x^2}$ included between the lines $x=0$ and $x=a$ is 4 sq units. Then the value of ' $a$ ' is

A

$\frac{16}{\sqrt{\pi}}$

B

$\frac{4}{\pi}$

C

$\frac{2}{\sqrt{\pi}}$

D

$\frac{4}{\sqrt{\pi}}$

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11

2025 · Mathematics · Calculus · Area Under The Curves

COMEDK 2025 Morning Shift

Area of the region bounded by the curve $y=\sin \left(\frac{x}{2}\right)$ between $-4 \pi$ and 0 is

A

4 sq units

B

8 sq units

C

6 sq units

D

1 sq units

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12

2025 · Mathematics · Calculus · Area Under The Curves

COMEDK 2025 Morning Shift

The area bounded by the parabola $y^2=36 x$ and its latus rectum is

A

216 sq units

B

108 sq units

C

27 sq units

D

54 sq units

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13

2026 · Mathematics · Calculus · Area Under The Curves

COMEDK 2026 Morning Shift

The area of the region bounded by the line $y=x+2$ and the curve $x=-y^2$ is

A

13.5 sq units

B

$\frac{7}{6}$ sq units

C

4.5 sq units

D

2.5 sq units

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14

2026 · Mathematics · Calculus · Area Under The Curves

COMEDK 2026 Morning Shift

The area of the region in the first quadrant enclosed by the $x$-axis, the line $x=\sqrt{3} y$ and the circle $x^2+y^2=4$ is

A

$\frac{\pi}{6}$ sq units

B

$\frac{2 \pi}{3}$ sq units

C

$\pi$ sq units

D

$\frac{\pi}{3}$ sq units

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15

2026 · Mathematics · Calculus · Area Under The Curves

COMEDK 2026 Afternoon Shift

The area enclosed by the curve $y=-x^2$ and the line $x+y+2=0$ is

A

$4.5 $ sq units

B

$3 .5$ sq units

C

$4 $ sq units

D

$5 .5$ sq units

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16

2026 · Mathematics · Calculus · Area Under The Curves

COMEDK 2026 Afternoon Shift

Find the area bounded by the curve $y=|2-x|$, the $x$-axis, and the lines $x=0$ and $x=5$

A

4.5 sq units

B

6.5 sq units

C

12 .5 sq units

D

8.5 sq units

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