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Through any point $(x, y)$ of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of

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Important Questions on Area under Curves

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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

HARD

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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

EASY

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

The area enclosed between the parabolas

y^{2} = 16 x

and

x^{2} = 16 y

HARD

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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>Area under Curves>Curve Tracing

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

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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

HARD

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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,

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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>Area under Curves>Curve Tracing

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>Area under Curves>Curve Tracing

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>Area under Curves>Curve Tracing

For a real numbers

x

, let

[x]

denote the largest number less than or equal

x .

For

x \in R

let

f (x) = [x] \sin π x

.Then

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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>Area under Curves>Curve Tracing

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>Area under Curves>Curve Tracing

On the real line

R

, we define two functions

f

and

g

as follows:

f (x) = m i n {x - [x], 1 - x + [x]}

g (x) = m a x \{x - [x], 1 - x + [x]\}

Where

[x]

denotes the largest integer not exceeding

x

. The positive integer

n

for which

\int_{0}^{n} (g (x) - f (x)) d x = 100

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

The area of the region bounded by the lines

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

and

x = 4

HARD

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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}\}

EASY

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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

HARD

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

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

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

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Curve Tracing

Consider the following parametric equation of a curve:

$x (θ) = |\cos 4 θ| cosθ$

$y (θ) = |\cos 4 θ| \sin θ$

For $0 \leq θ \leq 2 π$

Which one of the following graphs represents the curve?

Through any point x,y of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of

Important Questions on Area under Curves

Learn and Prepare for any exam you want !

Through any point $(x, y)$ of a curve which passes through the origin, lines are drawn parallel to the coordinate axes. The curve, given that it divides the rectangle formed by the two lines and the axes into two areas, one of which is twice the other, represents a family of