Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 2>Q 26

EASY

JEE Main/Advance

IMPORTANT

Earn 100

Area bounded by the curves $y = 2^{x}, y = 2 x - x^{2}$ , $x = 0$ and $x = 2$ is equal to

50% studentsanswered this correctly

Important Questions on Application of Integrals

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 2>Q 27

For which of the following positive value of

m

, the area of the region bounded by the curve

y = x - x^{2}

and the line

y = m x

equals

\frac{9}{2} ?

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 2>Q 28

The area bounded by the curve

y = (x - 1)^{2}

,

y = (x + 1)^{2}

and the

x

-axis is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 2>Q 29

The parabolas

x^{2} = 4 y

and

y^{2} = 4 x

divide the square region bounded by the lines

x = 4,

y = 4

and the coordinates axes. If

S_{1}, S_{2}, S_{3}

are respectively the areas of these parts numbered from top to bottom; then

S_{1} : S_{2} : S_{3}

is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 2>Q 30

The area of figure bounded by the curves

y = a^{x}

(a > 1)

and

y = b^{- x} (b > 1)

and the straight line

x = 1

is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 2>Q 31

Minimum area of the triangle formed by any tangent to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

with co-ordinate axes is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 2>Q 32

The area enclosed by the curves

y^{2} = x^{3}

and

| y | = 2 x

, in square units, is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 2>Q 33

The area bounded by curve

f (x) = | \tan x + \cot x | - | \tan x - \cot x |

between lines

x = 0, x = \frac{π}{2}

and

x

-axis, is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 2>Q 35

The area bounded by curve

f (x) = x^{3}

and

g (x) = \sqrt[3]{x}

is (in square units)