EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 31 August 2021 Shift 2>Q 3

MEDIUM

JEE Main

IMPORTANT

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If the line $y = m x$ bisects the area enclosed by the lines $x = 0, y = 0, x = \frac{3}{2}$ and the curve $y = 1 + 4 x - x^{2},$ then $12 m$ is equal to .

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Important Questions on Area under Curves

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 1 September 2021 Shift 2>Q 4

The area, enclosed by the curves

y = \sin x + \cos x

and

y = | \cos x - \sin x |

and the lines

x = 0, x = \frac{π}{2},

is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 20 July 2021 Shift 1>Q 5

Let

T

be the tangent to the ellipse

E : x^{2} + 4 y^{2} = 5

at the point

P (1, 1)

. If the area of the region bounded by the tangent

T

, ellipse

E

, lines

x = 1

and

x = \sqrt{5}

is

α \sqrt{5} + β + γ \cos^{- 1} (\frac{1}{\sqrt{5}})

, then

| α + β + γ |

is equal to______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 22 July 2021 Shift 1>Q 6

Let the area (in sq. units) of the region bounded by the curves

x^{2} + 2 y - 1 = 0, y^{2} + 4 x - 4 = 0

and

y^{2} - 4 x - 4 = 0

in the upper half plane be

k

, then the value of

k

is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 25 July 2021 Shift 1>Q 7

The area (in sq. units) of the region, given by the set

\{(x, y) \in R \times R ∣ x \geq 0, 2 x^{2} \leq y \leq 4 - 2 x\}

is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 27 July 2021 Shift 1>Q 8

If the area of the bounded region

R = \{(x, y) : \max \{0, \log_{e} x\} \leq y \leq 2^{x}, \frac{1}{2} \leq x \leq 2\}

is,

α {(\log_{e} 2)}^{- 1} + β (\log_{e} 2) + γ

then the value of

{(α + β - 2 γ)}^{2}

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main - 27 July 2021 Shift 2>Q 9

The area of the region bounded by

y - x = 2

and

x^{2} = y

is equal to :-

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main 17 March 2021 Shift 2>Q 10

Let

f : [- 3, 1] \to R

be given as

f (x) = \{\begin{array}{l} m i n \{(x + 6), x^{2}\}, & - 3 \leq x \leq 0 \\ m a x \{\sqrt{x}, x^{2}\}, & 0 \leq x \leq 1 \end{array} .

If the area bounded by

y = f (x)

and

x

-axis is

A

sq units, then the value of

6 A

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 30 - Area under Curves>JEE Main 18 March 2021 Shift 2>Q 11

The area (in sq. unit) bounded by the curve

4 y^{2} = x^{2} (4 - x) (x - 2)

is equal to