Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-2>Q 17

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Area bounded by $y = x^{2} - 2 |x|$ and $y = - 1$ is equal to

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Important Questions on Area under Curves

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-3>Q 1

Area of the region bounded by the curve

y = e^{x}

and lines

x = 0

and

y = e

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-3>Q 3

Let the straight line

x = b

divide the area enclosed by

y = {(1 - x)}^{2}, y = 0

and

x = 0

into two parts

R_{1} (0 \leq x \leq b)

and

R_{2} (b \leq x \leq 1)

such that

R_{1} - R_{2} = \frac{1}{4}

. Then

b

equals

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-3>Q 4

Let

f : [- 1, 2] \to [0, \infty)

be a continuous function such that

f (x) = f (1 - x) \forall x \in [- 1, 2]

. Let

R_{1} = \int_{- 1}^{2} x f (x) d x

and

R_{2}

be the area of the region bounded by

y = f (x), x = - 1, x = 2

and the

X -

axis. Then,

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-3>Q 5

The area enclosed by the curves

y = \sin x + \cos x

and

y = | \cos x - \sin x |

over the interval

[0, \frac{π}{2}]

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-3>Q 6

Area of the region

\{(x, y)\} \in R^{2} : y \geq \sqrt{| x + 3 |}, 5 y \leq (x + 9) \leq 15}

is equal to (in sq. units):

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-3>Q 8

A farmer

F_{1}

has a land in the shape of a triangle with vertices at

P (0, 0), Q (1, 1)

and

R (2, 0)

. From this land, a neighbouring farmer

F_{2}

takes away the region which lies between the side

P Q

and a curve of the form

y = x^{n} (n > 1)

. If the area of the region taken away by the farmer

F_{2}

is exactly

30 %

of the area of

∆ P Q R

, then the value of

n

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-3>Q 9

The area of the region bounded by the parabola

{(y - 2)}^{2} = x - 1

, the tangent to the parabola at the point

(2, 3)

and the

x -

aixs is

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Alpha Question Bank for Engineering: Mathematics>Chapter 31 - Area under Curves>Exercise-3>Q 10

The area bounded by the curves

y = \cos x

and

y = \sin x

between the ordinates

x = 0

and

x = \frac{3 π}{2}

is