Mathematics Crash Course JEE Main>Chapter 2 - Area under Curves>Level 3>Q 1

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IMPORTANT

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The area bounded by the curves $y = \cos^{- 1} x;$ $y = \sin^{- 1} x$ and $y = - π x^{3},$ where $- 1 \leq x \leq 1,$ is:

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Important Questions on Area under Curves

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 2 - Area under Curves>Level 3>Q 2

If

f (x) = \{\begin{cases} \sqrt{\{x\}} & for & x \notin Z \\ 1 & for & x \in Z \end{cases}

and

g (x) = {\{x\}}^{2}

where

\{\cdot\}

denotes fractional part of

x

, then area bounded by

f (x)

and

g (x)

for

x \in (0, 6)

is:

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 2 - Area under Curves>Level 3>Q 3

Let

S

is the region of points which satisfies

y^{2} < 16 x,

x < 4

and

\frac{x y (x^{2} - 3 x + 2)}{x^{2} - 7 x + 12} > 0

. Its area is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 2 - Area under Curves>Level 3>Q 4

The area bounded by the curves $- x \sqrt{3} + y = 2 \log_{e} (x + y \sqrt{3}) - 2 \log_{e} 2, y = \sqrt{3} x$ and $y = - \frac{1}{\sqrt{3}} x + 2$ is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 2 - Area under Curves>Level 3>Q 5

Area of region bounded by the curves

y = \frac{4 - x^{2}}{4 + x^{2}}

,

25 y^{2} = 9 x

and

y = \frac{3}{5} | x | - \frac{6}{5}

which contains

(1, 0)

point in its interior, is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 2 - Area under Curves>Level 3>Q 6

Area bounded by the curve

y^{2} (2 a - x) = x^{3}

and the line

x = 2 a

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 2 - Area under Curves>Level 3>Q 7

If the area bounded by the curves

2 y^{2} + x = 0, 3 y^{2} + x = 1

and

y

-axis in the second quadrant is

A

sq. units, then the value of

\frac{9 A}{3 - \sqrt{3}}

is equal to

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 2 - Area under Curves>Level 3>Q 8

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

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 2 - Area under Curves>Level 3>Q 9

Consider a line

ℓ : 2 x - \sqrt{3} y = 0

and a parametrised

C : x = \tan t, y = \frac{1}{\cos t} (0 \leq t < \frac{π}{2})

. If the area of part bounded by

ℓ, C

and the

y

-axis is equal to

\frac{1}{4} \ln (a + \sqrt{b})

, where

a, b, \in N, b

, is not perfect square then find the value of

(a + b)

.