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

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The area bounded by the curve $f(x)=x+\sin x$ and its inverse function between the ordinates $x=0$ and $x=2 \pi$, in square units, 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>EXERCISE>Q 10

The area bounded by the

x -

axis, the curve

y = f (x)

and the lines

x = 1

and

x = b

is equal to

\sqrt{b^{2} + 1} - \sqrt{2}

for all

b > 1,

then

f (x)

is

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 1>Q 1

Find area bounded by curve

y = x, x -

axis and

x = 1

(using integration).

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 1>Q 2

Find the area bounded by the curve

y^{2} = 4 a x

and its latus rectum.

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 1>Q 3

Find the area bounded by the curve

y = x^{3}

, the

x -

axis and the ordinates

x = - 2

and

x = 1

.

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 1>Q 4

Find the area bounded by the curve

y = \log_{e} x

, the

x -

axis and the straight line

x = e

.

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 1>Q 5

Find the area bounded by the circle

x^{2} + y^{2} = 16

and the line

y = x

in the first quadrant.

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 1>Q 6

Find the area bounded by the curve

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

and the line

y = 1 .

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Gamma Question Bank for Engineering Mathematics>Chapter 29 - Application of Integrals>Assignment Set - 1>Q 7

AOB

is the positive quadrant of the ellipse

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

where

OA = a, OB = b

. Then find the area between the arc

AB

and the chord

AB

of the ellipse.