Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 9 - Area>DPP>Q 15

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IMPORTANT

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If the area bounded between $x$ -axis and the graph of $y = 6 x - 3 x^{2}$ between the ordinates $x = 1$ and $x = a$ is $19$ square units, then $a$ can take

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Important Questions on Area

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JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 9 - Area>DPP>Q 16

Which of the following is the possible value/values of

c

for which the area of the figure bounded by the curves

y = \sin 2 x

, the straight lines

x = \frac{π}{6}, x = c

and the

x

-axis is equal to

1 / 2

sq. units ?

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 9 - Area>DPP>Q 17

Area (in sq. units) of the region bounded by the curve

y = \tan x

and lines

y = 0

and

x = 1

is

MEDIUM

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 9 - Area>DPP>Q 1

Suppose

y = f (x)

and

y = g (x)

are two functions whose graphs intersect at the three points

(0, 4), (2, 2)

and

(4, 0)

with

f (x) > g (x)

for

0 < x < 2

and

f (x) < g (x)

for

2 < x < 4

. If

\int_{0}^{4} [f (x) - g (x)] d x = 10

and

\int_{2}^{4} [g (x) - f (x)] d x = 5

, the area between two curves for

0 < x < 2

, is:

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 9 - Area>DPP>Q 2

The ratio of the areas of two regions of the curve

C_{1} \equiv 4 x^{2} + π^{2} y^{2} = 4 π^{2}

divided by the curve

C_{2} \equiv y = - (sgn (x - \frac{π}{2})) \cos x

, (where

sgn (x) = signum (x)

) is

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Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 9 - Area>DPP>Q 3

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

HARD

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 9 - Area>DPP>Q 4

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

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 9 - Area>DPP>Q 5

Area bounded by the

\min . \{|x|, |y|\} = 1

and the

\max . \{|x|, |y|\} = 2

is:

HARD

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IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Calculus JEE Main & Advanced>Chapter 9 - Area>DPP>Q 6

Consider

f (x) = \{\begin{cases} \cos x & ; 0 \leq x < \frac{π}{2} \\ {(\frac{π}{2} - x)}^{2} & ; \frac{π}{2} \leq x < π \end{cases}

such that

f

is periodic with period

π .

Then which of the following is not true?