The region represented by x - y ≤ 2 and x + y ≤ 2 is bounded by a

square of side length 2 2 units.

rhombus of area 8 2 sq . units .

rhombus of side length 2 units.

HARD

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The area bounded by the curve $y = x^{4} - 2 x^{3} + x^{2} + 3$ with $x$ -axis and ordinates corresponding to the minima of $y$ is

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Important Questions on Application of Integrals

HARD

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

Let

S (α) = \{(x, y) : y^{2} \leq x, 0 \leq x \leq α\}

and

A (α)

is area of the region

S (α) .

If for a

λ, 0 < λ < 4, A (λ) : A (4) = 2 : 5,

then

λ

equals:

HARD

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

The area bounded by

y = 1+ |x|, y = 0

and

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

will be

EASY

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

Area lying between the parabola

y^{2} = 4 a x

and its latus rectum is

EASY

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

The area enclosed by the curve

x = 3 cosθ, y = 2 sinθ, 0 \leq θ \leq π

, is (in square units)

HARD

Mathematics>Integral Calculus>Application of Integrals>Area Under Simple 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

HARD

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

The area (in sq units) of the quadrilateral formed by the tangents at the endpoints of the latus rectum to the ellipse $\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1$ is?

HARD

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

Let

g (x) = \cos x^{2}, f (x) = \sqrt{x},

and

α, β (α < β)

be the roots of the quadratic equation

18 x^{2} - 9 π x + π^{2} = 0

. Then the area (in sq. units) bounded by the curve

y = (g o f) (x)

and the lines

x = α, x = β

and

y = 0,

MEDIUM

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

The area of the region bounded by the line

y = 2 x + 1

x

-axis and the ordinates

x = - 1

and

x = 1

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,

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 of the region bounded by

y = | x |, y = 0, x = 3

and

x = - 3

is (in square units)

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

The area of the region bounded by the curve

y = \cos x, x = 0

and

x = π

MEDIUM

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

The region represented by

|x - y| \leq 2

and

|x + y| \leq 2

is bounded by a

MEDIUM

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

The area under the curve

y = |\cos x - \sin x|, 0 \leq x \leq \frac{π}{2}

and above

X

-axis, is

MEDIUM

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

The area enclosed (in square units) by the curve

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

, the

x

-axis and the vertical lines passing through the two minimum points of the curve is

MEDIUM

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

The area bounded by the parabola

x^{2} = 4 y

and the lines

y = 2, y = 4

and

y

-axis 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

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

EASY

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

The area of the region bounded by the curve

x = 2 y + 3

y

-axis, and lines

y = 1

and

y = - 1

The area bounded by the curve y=x4-2x3+x2+3 with x -axis and ordinates corresponding to the minima of y is

Important Questions on Application of Integrals

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The area bounded by the curve $y = x^{4} - 2 x^{3} + x^{2} + 3$ with $x$ -axis and ordinates corresponding to the minima of $y$ is