MEDIUM

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Let $y = f (x)$ be a curve which satisfies the differential equation $e^{x} d y + (x - 1) d x = 0$ and $f (0) = 0$ If the area enclosed by the curve, $x -$ axis, $y -$ axis and a line $x = c,$ $(c, f (c))$ is the point of inflection on the curve is $(1 - \frac{p}{e^{q}}) (p, q \in N),$ then the value of $(p + q)$ equals

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Important Questions on Area under Curves

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Area Bounded by Curves

Let

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

I

is minimum then the ordered pair

(a, b)

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Area Bounded by Curves

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

y = x^{2} - 1,

the tangent at the point

(2, 3)

to it and the

y

-axis is

HARD

Mathematics>Integral Calculus>Area under Curves>Area Bounded by 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

EASY

Mathematics>Integral Calculus>Area under Curves>Area Bounded by 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

HARD

Mathematics>Integral Calculus>Area under Curves>Area Bounded by Curves

Area of the region bounded by the curve

y^{2} = 4 x, y

-axis and the line

y = 3

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Area Bounded by 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

HARD

Mathematics>Integral Calculus>Area under Curves>Area Bounded by Curves

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

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

HARD

Mathematics>Integral Calculus>Area under Curves>Area Bounded by 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>Area under Curves>Area Bounded by Curves

Smaller area enclosed by the circle

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

and the line

x + y = 2

EASY

Mathematics>Integral Calculus>Area under Curves>Area Bounded by Curves

The area (in sq. units) of the region

{x \in R : x \geq 0, y \geq 0, y \geq x - 2

and

y \leq \sqrt{x}}

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Area Bounded by 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

HARD

Mathematics>Integral Calculus>Area under Curves>Area Bounded by Curves

The area bounded by

y = 1+ |x|, y = 0

and

|x| = \frac{1}{2}

will be

HARD

Mathematics>Integral Calculus>Area under Curves>Area Bounded by 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

HARD

Mathematics>Integral Calculus>Area under Curves>Area Bounded by 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

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Area Bounded by 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>Area under Curves>Area Bounded by Curves

The area enclosed between the parabolas

y^{2} = 16 x

and

x^{2} = 16 y

HARD

Mathematics>Integral Calculus>Area under Curves>Area Bounded by 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

MEDIUM

Mathematics>Integral Calculus>Area under Curves>Area Bounded by Curves

The area of the region bounded by

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

and the

y-

axis lying in the first quadrant is _______ square units.

HARD

Mathematics>Integral Calculus>Area under Curves>Area Bounded by Curves

The area bounded by

f (x) = x^{2}, 0 \leq x \leq 1, g (x) = - x + 2, 1 \leq x \leq 2

and

x

-axis is

EASY

Mathematics>Integral Calculus>Area under Curves>Area Bounded by Curves

The area of the region bounded by the curve

x = 2 y + 3

y

-axis, and lines

y = 1

and

y = - 1

Let y=f(x) be a curve which satisfies the differential equation exdy+(x-1)dx=0 and f(0)=0 If the area enclosed by the curve, x-axis, y-axis and a line x=c, (c,f(c)) is the point of inflection on the curve is 1-peq (p,q∈N), then the value of (p+q) equals

Important Questions on Area under Curves

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