Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment>Q 13

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The area of the region bounded by the curves $y = x^{2}$ and $y = \sec^{- 1} [- \cos^{2} x],$ where [.] represent greatest integer function, is

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Important Questions on Application of Integrals

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment>Q 14

If the area bounded by

x

-axis, the curve

y = f (x)

and the ordinates

x = c

and

x = d

is independent of

d, \forall d > c

(

c

is constant), then

f

is

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

The line

y = m x

bisects the area enclosed by the lines

x = 0, y = 0

and

x = \frac{3}{2}

and the curve

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

then the value of

m

is equal to

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment>Q 4

Let

A_{1}

be the area of the triangle with vertices

(0, 0), (0, c^{2}),

and

(c, c^{2})

and let

A_{2}

be the area of the region bounded by the line

y = c x, (c > 0)

and the curve

y = x^{2},

Then

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment>Q 6

The value(s) of

' m'

for which the area of the region bounded by the curve

y = x - x^{2}

and the line

y = m x

is

(\frac{9}{2})

sq.units, is/are

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment>Q 7

Consider two curves

C_{1} : y = e^{x}

and

C_{2} : y = e^{a - x},

where

' a'

is positive constant. Let

A

be the area of the part surrounding by

C_{1}, C_{2}

and the

y

-axis then

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment>Q 8

Let

f (x) = \min (\cos^{- 1} (\cos x), \cot^{- 1} (\cot x)), x \in (π, 2 π)

then which of the following statements are correct?

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment>Q 9

The three curves

y = \sqrt{x}, x = - \sqrt{y}

and

x^{2} + y^{2} = 2

are given then the area

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment>Q 10

Two curves

f (x) = \cos x

and

g (x) = 1 + \sin 2 x,

where

x \in (0, \frac{3 π}{2})

are given then