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.

Let, n ≥ 2 be a natural number and 0 < θ < π 2 . Then ∫ s i n n θ - s i n θ 1 n c o s θ s i n n + 1 θ d θ , is equal to

n n 2 - 1 1 - 1 s i n n - 1 θ n + 1 n + c

n n 2 - 1 1 - 1 s i n n + 1 θ n + 1 n + c

n n 2 + 1 1 - 1 s i n n - 1 θ n + 1 n + c

n n 2 - 1 1 + 1 s i n n - 1 θ n + 1 n + c

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Important Questions on Integrals

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Mathematics>Integral Calculus>Integrals>Methods of Integration

The region represented by

|x - y| \leq 2

and

|x + y| \leq 2

is bounded by a

MEDIUM

Mathematics>Integral Calculus>Integrals>Methods of Integration

The area (in sq. units) of the region

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

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

If the area (in sq. units) of the region

\{(x, y) : y^{2} \leq 4 x, x + y \leq 1, x \geq 0, y \geq 0\}

a \sqrt{2} + b,

then

a - b

is equal to

EASY

Mathematics>Integral Calculus>Integrals>Methods of Integration

Using integration, find the area of the region bounded by the triangle whose vertices are

(2, - 2), (4, 5) and (6, 2)

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

Diagrammatic representation of the operation of natural selection two peaks are formed. This condition shows _____ effects.

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

Using integration, find the area of the triangle

A B C

whose vertices have coordinate

A (2, 5), B (4, 7)

and

C (6, 2)

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Mathematics>Integral Calculus>Integrals>Methods of Integration

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

y = 2^{x}

and

y = |x + 1|

, in the first quadrant is

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

Area of the region bounded by the curve

y^{2} = 4 x, y

-axis and the line

y = 3

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

Phylogenetic relationship among plants $(P, Q, R, S)$ based on their shared characters is shown in the cladogram below.
Identify the plants $P, Q, R$ and $S$ in the correct order.

Question Image

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Mathematics>Integral Calculus>Integrals>Methods of Integration

Let

A = \{(x, y) : y^{2} \leq 4 x, y - 2 x \geq - 4\}

. The area of the region

A

in square units is

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

Using integration, find the area of the region bounded by the triangle whose vertices are

(1, 0), (2, 2) and (3, 1)

EASY

Mathematics>Integral Calculus>Integrals>Methods of Integration

f (x) = x + 1

, find

\frac{d}{d x} (fof) (x)

EASY

Mathematics>Integral Calculus>Integrals>Methods of Integration

Find the area of the parabola

y^{2} = 4 a x

bounded by its latus rectum.

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Mathematics>Integral Calculus>Integrals>Methods of Integration

Area bounded by the curve

y = x^{3}, x

-axis and the ordinates at

x = - 2

and

x = 1

, is

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

Smaller area enclosed by the circle

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

and the line

x + y = 2

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

The integral

\int \frac{3 x^{13} + 2 x^{11}}{{(2 x^{4} + 3 x^{2} + 1)}^{4}} d x

, is equal to

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

Let,

n \geq 2

be a natural number and

0 < θ < \frac{π}{2} .

Then

\int \frac{{(s i n^{n} θ - s i n θ)}^{\frac{1}{n}} c o s θ}{s i n^{n + 1} θ} d θ,

is equal to

HARD

Mathematics>Integral Calculus>Integrals>Methods of Integration

The area of the region

(

in square units

)

above the

x

-axis bounded by the curve

y = \tan x, 0 \leq x \leq \frac{π}{2}

and the tangent to the curve at

x = \frac{π}{4}

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Mathematics>Integral Calculus>Integrals>Methods of Integration

During evolution _____ evolved into first amphibians.

EASY

Mathematics>Integral Calculus>Integrals>Methods of Integration

For

x ϵ (0, \frac{3}{2}),

let

f (x) = \sqrt{x}, g (x) = t a n x

and

h (x) = \frac{1 - x^{2}}{1 + x^{2}}

. If

ϕ (x) = (h o f) o g) (x),

then

ϕ (\frac{π}{3})

is equal to:

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Important Questions on Integrals

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