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The area bounded by a curve, the axis of co-ordinates and the ordinate of some point of the curve is equal to the length of the corresponding arc of the curve. If the curve passes through the point $P (0, 1)$ , then the equation of this curve can be

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Important Questions on Application of Integrals

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area (in sq. unit) of the region described by

A = \{(x, y) : x^{2} + y^{2} \leq 1 and y^{2} \leq 1 - x\}

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

Consider two straight lines, each of which is tangent to both the circle

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

and the parabola

y^{2} = 4 x

. Let these lines intersect at the point

Q

. Consider the ellipse whose center is at the origin

O (0, 0)

and whose semi-major axis is

O Q

. If the length of the minor axis of this ellipse is

\sqrt{2}

, then which of the following statement(s) is (are) TRUE?

MEDIUM

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area (in square units) of the region bounded by the curves

y + 2 x^{2} = 0

and

y + 3 x^{2} = 1

, is equal to

EASY

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area of region bounded by the lines

y = m x, x = 1

and

x = 2

and the

x

-axis is

7.5

sq. units, then

m

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

If the area enclosed between the curves

y = k x^{2}

and

x = k y^{2}, (k > 0),

1 s q . u n i t .

Then

k

EASY

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area enclosed between the parabolas

y^{2} = 16 x

and

x^{2} = 16 y

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area (in square units) bounded by the curves $y = \sqrt{x}, 2 y - x + 3 = 0$ , $X$ -axis and lying in the first quadrant is

MEDIUM

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area of the region bounded by the lines

y = 2 x + 1, y = 3 x + 1

and

x = 4

EASY

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area (in sq. units) of the region bounded by the parabola,

y = x^{2} + 2

and the lines,

y = x + 1, x = 0

and

x = 3

, is

MEDIUM

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area of the region

A = {(x, y) : 0 \leq y \leq x |x| + 1 and - 1 \leq x \leq 1}

in sq. units, is

MEDIUM

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

If the area of the region bounded by the curves,

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

and the lines

y = 0

and

x = t (t > 1)

1 sq . unit

, then

t

is equal to

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

Area of the region

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

5 y \leq x + 9 \leq 15}

is equal to

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area of the region bounded by the curve

y = |x^{3} - 4 x^{2} + 3 x|

and the

x

-axis,

0 \leq x \leq 3,

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The parabola

y^{2} = 4 x + 1

divides the disc

x^{2} + y^{2} \leq 1

into regions with areas

A_{1}

and

A_{2} .

Then

|A_{1} - A_{2}|

equals

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area (in sq. units) of the region

\{(x, y) : x \geq 0, x + y \leq 3, x^{2} \leq 4 y a n d y \leq 1 + \sqrt{x}\}

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area (in sq. units) of the smaller portion enclosed between the curves,

x^{2} + y^{2} = 4

and

y^{2} = 3 x

, is:

MEDIUM

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area( in sq. units) bounded by

y = \sin^{2} x, x = \frac{π}{2}

and

x = π

MEDIUM

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

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

MEDIUM

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

Let

I = \int_{a}^{b} (x^{4} - 2 x^{2}) d x .

I

is minimum then the ordered pair

(a, b)

HARD

Mathematics>Integral Calculus>Application of Integrals>Area under Simple Curves

The area (in sq. units) of the region described by

[(x, y) : y^{2} \leq 2 x and y \geq 4 x - 1]

The area bounded by a curve, the axis of co-ordinates and the ordinate of some point of the curve is equal to the length of the corresponding arc of the curve. If the curve passes through the point P0,1, then the equation of this curve can be

Important Questions on Application of Integrals

Learn and Prepare for any exam you want !

The area bounded by a curve, the axis of co-ordinates and the ordinate of some point of the curve is equal to the length of the corresponding arc of the curve. If the curve passes through the point $P (0, 1)$ , then the equation of this curve can be