## Chapter 21 – Areas of bounded regions Exercise Ex. 21.1

Thus, Required area = square units

and evaluate the area of the region under the curve and above the x-axis.

Sketch

the region {(x, y):9x^{2} + 4y^{2} = 36} and find the area

enclosed by it, using integration.

9x^{2} + 4y^{2} =

36

Area of Sector OABCO =

Area of the whole figure = 4 × Ar. D

OABCO

= 6p

sq. units

What dose this integral represent on the graph?.

Find the area of the minor segment of the circle x^{2} + y^{2} = a^{2} cut off by the line x =

Find the area of the region bounded by the curve x = at^{2}, y = 2at between the ordinates corresponding t = 1 and t = 2.

Find the area enclosed by the curve x = 3 cost,

y = 2 sin t.

## Chapter 21 – Areas of Bounded Regions Exercise Ex. 21.2

Find

the area of the region bounded by x^{2} = 4ay and its latusrectum.

Find

the area of the region bounded by x^{2} + 16y = 0 and its latusrectum.

Find the area of the region bounded by the curve ay^{2} = x^{3}, the y-axis and the lines y = a and y = 2a.

## Chapter 21 – Areas of Bounded Regions Exercise Ex. 21.3

Calculate the area of the region bounded by the parabolas y^{2} = 6x and x^{2} = 6y.

Find

the area of the region common to the parabolas 4y^{2} = 9x and 3x^{2}

= 16y.

Find the area of the region between the circles x^{2} + y^{2} = 4 and (x – 2)^{2} + y^{2} = 4.

Find the area of the region bounded by y =, x = 2y + 3 in the first quadrant and x-axis.

Using

Integration, find the area of the region bounded by the triangle whose

vertices are (– 1, 2), (1, 5) and (3,

4).

Equation of side AB,

Equation of side BC,

Equation of side AC,

Area of required region

= Area of EABFE + Area of BFGCB –

Area of AEGCA

Find the area of the bounded by y =and y = x.

Find the area enclosed by the curve y = -x^{2} and the straight line x + y + 2 = 0.

Using the method of integration, find the area of the region bounded by the following lines: 3x – y – 3 = 0,

2x + y – 12 = 0, x – 2y – 1 = 0.

Find the area of the region enclosed by the parabola

x^{2} = y and the line y = x + 2.

## Chapter 21 – Areas of Bounded Regions Exercise Ex. 21.4

Find the area of the region between the parabola x = 4y – y^{2} and the line x = 2y – 3.

Find the area bounded by the parabola x = 8 + 2y – y^{2}; the y-axis and the lines y = -1 and y = 3.

Find the area bounded by the parabola y^{2} = 4x and the line

y = 2x – 4.

i. By using horizontal strips

ii. By using vertical strips

Find the area of the region bounded the parabola y^{2} = 2x and straight line x – y = 4.

## Chapter 21 – Areas of Bounded Regions Exercise MCQ

a. 1/ 2

b. 1

c. -1

d. 2

Correct option: (b)

The area included between the parabolas y^{2}=4x and x^{2} = 4y is (in square units)

a. 4/3

b. 1/3

c. 16/3

d. 8/3

Correct option: (c)

The area bounded by the curve y= log_{e} x and x-axis and the straight line x =e is

- e. sq. units
- 1 sq. units

Correct option: (b)

The area bounded by y=2-x^{2} and x + y =0 is

Correct option: (b)

The area bounded by the parabola x =4 -y^{2} and y-axis, in square units, is

Correct option: (b)

If A_{n }be the area bounded by the curve y = (tan x)^{n} and the lines x = 0, y =0 and x =π /4, then for x > 2

Correct option: (a)

The area of the region formed by x^{2}+y^{2}-6x-4y+12 ≤ x and x ≤ 5/2 is

Correct option: (c)

a. 2

b. 1

c. 4

d. None of these

Correct option: (a)

The area of the region bounded by the parabola (y-2)^{2} =x-1 , the tangent to it at the point with the ordinate 3 and the x-axis is

- 3
- 6
- 7
- None of these

Correct option: (d)

NOTE: Answer not matching with back answer.

The area bounded by the parabola y^{2} = 4ax and x^{2} = 4 ay is

Correct option: (b)

The area bounded by the curves y = sin x between the ordinates x =0 , x =π and the x-axis is

- 2 sq. units
- 4 sq. units
- 3 sq. units
- 1 sq. units

Correct option: (a)

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

Correct option: (b)

The area bounded by the parabola y^{2}=4ax, latus rectum and x-axis is

Correct option: (b)

Correct option: (c)

NOTE: Answer not matching with back answer.

The area common to the parabola y = 2x^{2 }and y=x^{2}+4 is

Correct option: (c)

The area of the region bounded by the parabola y=x^{2}+1 and the straight line x + y =3 is give by

Correct option: (d)

The ratio of the areas between the curves y= cos x and y = cos 2x and x-axis from x =0 to x = π/3 is

- 1:2
- 2:1
- None of these

Correct options: (d)

NOTE: Answer not matching with back answer.

The area between x-axis and curve y = cos x when 0 ≤ x ≤ 2 π is

- 0
- 2
- 3
- 4

Correct option: (d)

Area bounded by parabola y^{2}=x and staright line 2y = x is

- 4/3
- 1
- 2/3
- 1/3

Correct option: (a)

NOTE: Options are modified.

The area bounded by the curve y = 4x-x^{2} and x-axis is

Correct option: (c)

Area enclosed between the curve y^{2}(2a-x)=x^{3} and the line x =2a above x-axis is

Correct option: (b)

The area of the region (in square units)bounded by the curve x^{2}=4y, line x =2 and x-axis is

- 1
- 2/3
- 4/3
- 8/3

Correct option: (b)

The area bounded by the curve y=f (x), x-axis, and the ordinates x =1 and x=b is (b-1) sin (3b+4). Then, f (x) is

- (x-1) cos (3x+4)
- Sin (3x+4)
- Sin (3x+4)+3(x-1)cos (3x+4)
- None of these

Correct option: (c)

The area bounded by the curve y^{2} =8x and x^{2}=8y is

NOTE: Answer is not matching with back answer.

The area bounded by the parabola y^{2}=8x, the x-axis, and the latus rectum is

Correct option: (a)

NOTE: Answer is not matching with back answer.

Area bounded by the curve y=x^{3}, the x-axis and the ordinates x =-2 and x =1 is

Correct option: (d)

The area bounded by the curve y = x |x| and the ordinates x =-1 and x = 1 is given by

Correct option: (c)

Correct option:(b)

The area of the circle x^{2} +y^{2}=16 interior to the parabola y^{2}=6x is

Correct option: (c)

Smaller area enclosed by the circle x^{2}+y^{2}=4 and the line x + y =2 is

- 2(π-2)
- π-2
- 2π-1
- 2(π+2)

Correct option: (b)

Area lying between the curves y^{2}=4x and y = 2x is

Correct option: (b)

Area lying in first quadrant and bounded by the circle x^{2}+y^{2}=4 and the lines x =0 and x =2, is

Correct option: (a)

Area of the region bounded by the curve y^{2}=4x ,y-axis and the line y =3, is

Correct option: (b)