##### Question 1:

Find the area of the region bounded by the curve y^{2} = x and the lines x = 1, x = 4 and the x-axis.

##### Answer:

y^{2} = x is right-handed parabola.

##### Question 2:

Find the area of the region bounded by y^{2} = 9x, x = 2, x = 4 and the x-axis in the first quadrant.

##### Answer:

The given parabola is y^{2} = 9x ..(1)

##### Question 3:

Find the area of the region bounded by x^{2} = 4y, y = 2, y = 4 and the y-axis in the first quadrant.

##### Answer:

x^{2} = 4y dx is an upward parabola.

##### Question 4:

##### Answer:

##### Question 5:

##### Answer:

##### Question 6:

##### Answer:

##### Question 7:

##### Answer:

##### Question 8:

The area between x = y^{2} and x = 4 is divided into two equal parts by the line x = a, find the value of a.

##### Answer:

We have : x = y^{2} ....(1)

and x = 4 ...(2)

##### Question 9:

Find the area of the region bounded by the parabola y = x^{2} and y = | x |.

##### Answer:

The given parabola is x^{2} = y ...(1)

This is an upward parabola with vertex (0, 0).

y = | x | represents the st. lines :

y = x and y = –x ...(2)

y = x meets (1) at O (0, 0) and A (1, 1)

y = – x meets (1) at O (0, 0) and A¢ (– 1, 1).

\ Reqd. area = 2 (Shaded area in first quadrant)

##### Question 10:

Find the area bounded by the curve x^{2} = 4y and the line x = 4y – 2.

##### Answer:

The given curve is x^{2} = 4y ...(1),

which is an upward parabola with vertex (0, 0).

The given line is x = 4y – 2 ...(2)

Solving (1) and (2) :

##### Question 11:

Find the area of the region bounded by the curve y^{2} = 4x and the line x = 3.

##### Answer:

The given curve is y^{2} = 4x ...(1)

and the given line is x = 3 ...(2)

Reqd. area = Shaded area

##### Question 12:

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

- $\mathrm{\pi}$

##### Answer:

$\mathrm{\pi}$

##### Question 13:

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

- 2

##### Answer:

##### Question 14:

Find the area of the circle 4x^{2} + 4y^{2} = 9, which is interior to the parabola x^{2} = 4y.

##### Answer:

The given circle is 4x^{2} + 4y^{2} = 9

##### Question 15:

Find the area bounded by curves :

(x – 1)^{2}+ y

^{2}= 1 and x

^{2}+ y

^{2}= 1.

##### Answer:

The given circles are :

x^{2} + y^{2} = 1 ....(1)

and (x – 1)^{2} + y^{2} = 1 ....(2)

(1) is a circle with centre (0, 0) and radius 1.

(2) is a circle with centre (1, 0) and radius 1.

Solving (1) and (2) :

##### Question 16:

Find the area bounded by the curves :

y = x^{2} + 2, y = x, x = 0 and x = 3.

##### Answer:

y = x^{2} + 2 is a parabola.

For tracing, we have the table :

##### Question 17:

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

(– 1, 0), (1, 3) and (3, 2).

##### Answer:

Let A (– 1, 0), B (1, 3) and C (3, 2) be the

vertices of the triangle as shown in the figure.

##### Question 18:

Using integration, find the area of the triangular region whose sides have the equations :

y = 2x + 1, y = 3x + 1 and x = 4.

##### Answer:

The given lines are :

y = 2x + 1 ...(1)

y = 3x + 1 ...(2)

and x = 4 ...(3)

Solving (1) and (2) : we get x = 0, y = 1.

Thus lines (1) and (2) intersect at A (0, 1).

Similarly lines (2) and (3) intersect at B (4, 13)

and lines (3) and (1) intersect at C (4, 9). [Do it]

##### Question 19:

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

- 2 ($\mathrm{\pi}$ – 2)
- $\mathrm{\pi}$ – 2
- 2$\mathrm{\pi}$ – 1
- 2 ($\mathrm{\pi}$ + 2)

##### Answer:

$\mathrm{\pi}$ – 2

##### Question 20:

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

##### Answer:

##### Question 21:

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

- $\mathrm{\pi}$

##### Answer:

$\mathrm{\pi}$

##### Question 22:

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

- 2

##### Answer:

##### Question 23:

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

- 2 ($\mathrm{\pi}$ – 2)
- $\mathrm{\pi}$ – 2
- 2 $\mathrm{\pi}$ – 1
- 2 ($\mathrm{\pi}$ + 2)

##### Answer:

$\mathrm{\pi}$ – 2

##### Question 24:

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

##### Answer:

##### Question 25:

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

- – 9

##### Answer:

##### Question 26:

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

- 0

##### Answer:

##### Question 27:

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

##### Answer:

##### Question 28:

The area enclosed by the circle x^{2} + y^{2} = 2 is equal to :

- 4$\mathrm{\pi}$ sq. units
- 4$\mathrm{\pi}$
^{2}sq. units - 2$\mathrm{\pi}$ sq. units.

##### Answer:

2$\mathrm{\pi}$ sq. units.

##### Question 29:

The area enclosed by the circle x^{2} + y^{2} = 2 is equal to :

- 4$\mathrm{\pi}$ sq. units
- 4$\mathrm{\pi}$
^{2}sq. units - 2$\mathrm{\pi}$ sq. units.

##### Answer:

2$\mathrm{\pi}$ sq. units.

##### Question 30:

- $\mathrm{\pi}$
^{2}ab - $\mathrm{\pi}$ ab
- $\mathrm{\pi}$a
^{2}b - $\mathrm{\pi}$ab
^{2}

##### Answer:

$\mathrm{\pi}$ab

##### Question 31:

The area of the region bounded by the curve y = x^{2} and the line y = 16 is :

##### Answer:

##### Question 32:

##### Answer:

##### Question 33:

The area of the region bounded by the curve x^{2} = 4y and the straight line x = 4y – 2 is :